Okay, so this is probably too late, but anyway
Can anyone explain optimization to me! Tomorrow morning?...ish...maybe?
I've tried getting people to explain it but they either WON'T help me or CAN'T help me and since I missed today, I couldn't get B-Rob to help =/
I've been stressing all day..crying for the majority of the time....stressing some more...and I have finally decided that I don't care anymore. I've tried my hardest and that's that. =]
Also, these study guides are great for telling me that I have no idea what I'm doing on a lot of these and that I actually have somewhat of a clue on others...I LOVE MULTIPLE CHOICE! =] (no sarcasm)
Stay on the bright side kids.
If anyone else is terrified for this exam, reply with Aye :)
(BTW: Not meant to sound whiney, just venting...my gosh I needed that... and trying to figure out Optim.)
Tuesday, October 13, 2009
Sunday, October 11, 2009
Post # 8
This week, since we did not go over anything new, I am going to show you how to use the Second Derivative Test to find all possible points of inflection and intervals of concavity. Remember, points of inflection only happen where there is a change of concavity.
Example: f'(x)= 6/(x^(2)+3)
First, you have to take the derivative of that, and you have to use the quotient rule, so the beginning of the problem will look like, [(x^(2)+3)(0)-6(2x)]/(x^(2)+3)^(2), which simplifies to -12x/(x^(2)+3)^2 remember, that was just the first derivative.
Second step is to take the derivative of the first derivative, that would make this step called taking the second derivative.
Once again u need to use the quotient rule, so f''(x)={(x2+3)^(2) -(12)-[(-12x)2(x^(2)+3)2x} all that over (x^(2)+3)^4 then you get a bunch of stuff, then you simplify, then you cancel, and if I typed all that up it would be ridiculous, so I'm just going to type the end answer of the second derivative. Which is, (3)(6)(x+1)(x-1) all over (x^(2)+3)^3
The possible points of inflection are found in the numerator of the finished second derivative, in this case, if you look, it would be x=1, and x=-1
so then you set up your points, (-infinity, -1) u (-1, 1) u (1, infinity)
then you plug in. f''(-2)= positive value f''(0)=negative value f''(2)=positive value
then you know that your intervals concave up @ (-infinity, -1) u (1,infinity) or x<1,>1
and it is concave down @ (-1,1) or -1
and you're points of inflection are x=-1, and x=1
okay, my question comes from a quiz that we had, it was the last problem and I didn't know how to do it, the problem goes like this: The sum of the perimeters of two squares is 24. Find the dimensions of the squares that produce the minimum total area.
I know it's a optimization problem, but I just don't know how to solve it. Help would be appreciated.
Example: f'(x)= 6/(x^(2)+3)
First, you have to take the derivative of that, and you have to use the quotient rule, so the beginning of the problem will look like, [(x^(2)+3)(0)-6(2x)]/(x^(2)+3)^(2), which simplifies to -12x/(x^(2)+3)^2 remember, that was just the first derivative.
Second step is to take the derivative of the first derivative, that would make this step called taking the second derivative.
Once again u need to use the quotient rule, so f''(x)={(x2+3)^(2) -(12)-[(-12x)2(x^(2)+3)2x} all that over (x^(2)+3)^4 then you get a bunch of stuff, then you simplify, then you cancel, and if I typed all that up it would be ridiculous, so I'm just going to type the end answer of the second derivative. Which is, (3)(6)(x+1)(x-1) all over (x^(2)+3)^3
The possible points of inflection are found in the numerator of the finished second derivative, in this case, if you look, it would be x=1, and x=-1
so then you set up your points, (-infinity, -1) u (-1, 1) u (1, infinity)
then you plug in. f''(-2)= positive value f''(0)=negative value f''(2)=positive value
then you know that your intervals concave up @ (-infinity, -1) u (1,infinity) or x<1,>1
and it is concave down @ (-1,1) or -1
and you're points of inflection are x=-1, and x=1
okay, my question comes from a quiz that we had, it was the last problem and I didn't know how to do it, the problem goes like this: The sum of the perimeters of two squares is 24. Find the dimensions of the squares that produce the minimum total area.
I know it's a optimization problem, but I just don't know how to solve it. Help would be appreciated.
post # eight
this week we reviewed.
Things that i do understand:
Tangent LIne- its simple. First step is to take a derivative, second plug in x value into that derivative, then you will get a slope. From there you take your slope and point and plug into the line formula.
Things that i dont understand.
I need more work with the limits and work with the optimization stuff. I get how to do optimizatin i know the steps i just always mess up getting the primary and/or secondary formula.
Things that i do understand:
Tangent LIne- its simple. First step is to take a derivative, second plug in x value into that derivative, then you will get a slope. From there you take your slope and point and plug into the line formula.
Things that i dont understand.
I need more work with the limits and work with the optimization stuff. I get how to do optimizatin i know the steps i just always mess up getting the primary and/or secondary formula.
posting..#8
This week in math we didn’t learn anything new we just did our presentations and our study packets for our test that’s on Wednesday. Although we didn’t learn anything new ill recap you on the steps of
Optimization
1 Identify primary and secondary equations your primary is the one your or maximizing or minimizing and your secondary is the other equation
2. Solve for your secondary variable and plug into your primary equation if your primary only has on variable this isn’t necessary
3. Plug into secondary equation to find the other value check your end points if necessary
Those are the steps of optimization hope that helped if you needed the recapped or you missed the notes.
What I need help on is Rolles theorem, mean value theorem and the intermediate value theorem. I don’t understand the first two but the intermediate value I can grasp I just would like a little help in remembering it.
But that’s it for me this week
Optimization
1 Identify primary and secondary equations your primary is the one your or maximizing or minimizing and your secondary is the other equation
2. Solve for your secondary variable and plug into your primary equation if your primary only has on variable this isn’t necessary
3. Plug into secondary equation to find the other value check your end points if necessary
Those are the steps of optimization hope that helped if you needed the recapped or you missed the notes.
What I need help on is Rolles theorem, mean value theorem and the intermediate value theorem. I don’t understand the first two but the intermediate value I can grasp I just would like a little help in remembering it.
But that’s it for me this week
Post 8
This week in calculus was pretty much a review week. We worked on the six review packets given to us for the exam. They helped me to understand some of the things I wasn't very clear on at the beginning of the nine weeks such as limits and tangent lines.
For limits, I was always so confused on how to figure out what the the limit was as it went to a certain number. I knew that one way to figure out the limit was to plug the number into x, but most of the time when I did this, the denominator of the limit would turn out to be zero, which left the limit undefined. I also knew that I could factor out my limit and maybe cross some things out, but sometimes this wouldn't work. This week I finally understood how to see what a certain limit is approaching using a table.
To see what the limit is approaching using a calculator, you use these steps:
1. Plug the limit equation into y= in your calculator
2. Go to your table function in your calculator and start plugging in values for the left and right of the number
3. When plugging in values, you will see the values will come very close to a particular number. This is your answer.
I also understood tangent lines. If an equation and an x value are given to you and the problem asks for a tangent line equation, you use these steps:
1. Plug the x value into your origional function to get your y value
2. Take the derivative of your function and plug your x value in to get your slope
3. Once you have an x value, a y value, and a slope, plug they all into point-slope form
I don't really have any questions this week except in need more help on my packets?
For limits, I was always so confused on how to figure out what the the limit was as it went to a certain number. I knew that one way to figure out the limit was to plug the number into x, but most of the time when I did this, the denominator of the limit would turn out to be zero, which left the limit undefined. I also knew that I could factor out my limit and maybe cross some things out, but sometimes this wouldn't work. This week I finally understood how to see what a certain limit is approaching using a table.
To see what the limit is approaching using a calculator, you use these steps:
1. Plug the limit equation into y= in your calculator
2. Go to your table function in your calculator and start plugging in values for the left and right of the number
3. When plugging in values, you will see the values will come very close to a particular number. This is your answer.
I also understood tangent lines. If an equation and an x value are given to you and the problem asks for a tangent line equation, you use these steps:
1. Plug the x value into your origional function to get your y value
2. Take the derivative of your function and plug your x value in to get your slope
3. Once you have an x value, a y value, and a slope, plug they all into point-slope form
I don't really have any questions this week except in need more help on my packets?
I'll just go over Instantaneous and average speed since no one seems to really have done that yet.
A wolf runs at y=93+2.3(t)^2 miles in t hours. What is it’s average speed during the first 5 seconds?
- State the slope formula: (y2-y1)/(x2-x1)
- Put the time you need to find into parenthesis or brackets: [0, 5] These are your two x’s.
- Plug x1 into your formula: y=93+2.3(0)^2 = 93 93 is your y1
- Plug x2 into your formula: y=93+2.3(5)^2=150.5 150.5 is your y2
- Plug back into your slope formula: (150.5-93)/(5-0)
- Simplify: 11.5 miles per hour
We can just use the same one for instantaneous speed.
- What is the instantaneous speed for t=3?
State the Instantaneous Speed formula:
Lim f(t-h)-f(t)
H->0 h - In the original problem, replace y with f(t): f(t)=93+2.3(t)2
- Plug in: Lim 93+2.3(3-h)^2-93+2.3(3)^2
H->0 h - Foil the parenthesis:
Lim 93+2.3(9-6h+h^2)-93+2.3(9)
H->0 h - Simplify:
Lim (93+20.7 –13.8h+2.3h^2) – (93 + 20.7)
H->0 h - Once you get it in it's simplest form, plug in for h.
Lim 2.3(0)+27.6
H->0 - ANSWER: 27.6 miles per hour.
For what i don't understand..i thought i understood limits, but idk what my deal is this week.
When it says is the limit of f(x) or f(2) larger.. what exactly am i doing.. i think
its one of the first questions on the ch. 1 study guide.
Post #8
Eight weeks down, many to go. This week in calculus, we presented and worked on our packets all week, so we really didn't learn anything new. I did learn that the table function on your calculator is a life saver and can be used to answer many problems.
To use your table function you have to plug in your equation to y equals and then press table which is second graph. If you are looking for the lim as it approaches -2, you will plug in numbers left to -2 and numbers right to -2.
Ex: -2-.1, -2-.01, -2-.001 for left and -2+.1, -2+.01, -2+.001 for the right side
You then have to see where each set of numbers are approaching to find the limit.
I also would like to remind everyone how to find rate of change because I had to learn it to complete chapter 3. To find the rate of change you have to plug into the formula f(b)-f(a)/b-a.
Ex: f(x) = x^3 + 9x on [1,3] and you are asked to find the average rate of change in f on [1,3].
f(3) = (3)^3 + 9(3) = 54
f(1) = (1)^3 + 9(1) = 10
54-10/ 3-1 = 44/2 = 22
One thing I am still confused on is how to find the formulas for optimization. I understand the steps once given the equations but I cannot figure out the formulas on my own.
I also do not understand b on number 9 chapter 3. I know y=125 but can't be 125 because it cannot exceed 100, so I do not know what to do next to get the correct answer.
To use your table function you have to plug in your equation to y equals and then press table which is second graph. If you are looking for the lim as it approaches -2, you will plug in numbers left to -2 and numbers right to -2.
Ex: -2-.1, -2-.01, -2-.001 for left and -2+.1, -2+.01, -2+.001 for the right side
You then have to see where each set of numbers are approaching to find the limit.
I also would like to remind everyone how to find rate of change because I had to learn it to complete chapter 3. To find the rate of change you have to plug into the formula f(b)-f(a)/b-a.
Ex: f(x) = x^3 + 9x on [1,3] and you are asked to find the average rate of change in f on [1,3].
f(3) = (3)^3 + 9(3) = 54
f(1) = (1)^3 + 9(1) = 10
54-10/ 3-1 = 44/2 = 22
One thing I am still confused on is how to find the formulas for optimization. I understand the steps once given the equations but I cannot figure out the formulas on my own.
I also do not understand b on number 9 chapter 3. I know y=125 but can't be 125 because it cannot exceed 100, so I do not know what to do next to get the correct answer.
post number 8
Wow, 8 weeks into the school year. sounds like a long time. this week was just reviewing for our exam which is in two parts on wednesday and thursday of this week, wednesday we are taking the multiple choice part of the exam. and on thursday we are taking the free response section, which mrs. robinson helped me abbey stephanie and trina with today at her house :) i would tell you what's on it, but you should've came to the study group.
ok, ill stop being mean now, and lets talk about calculus. at the study group today, i learned a lot about the process of elimination when it comes to multiple choice questions. also, if there is nothing else you can do with a problem that gives you a function and asks you to find something on a certain interval, like find the absolute extrema on the interval [0,2pi], then you can plug it into your calculator if you absolutely cannot figure it out by hand. also, short cuts are your friend :) like using the table function for problems like these. all of this really helped on the chap. 3 multiple choice part of our study guide.
some things i understand now are how to find a tangent line. the rules of finding a limit approaching infinity. how to take simple derivatives. instantaneous and average speed. all of these things. also how to look a a graph of a function and be able to know what the graph of the derivative of that function will look like, thank you dylan becnel :) haha. i also understand rolle's theorem and mean value theorem very well. what should i explain today? i think i'll explain how to look at the graph of a function and be able to know what the graph of the derivative of that function will look like.
Example:
let's say you are given the graph of a horizontal line. well, you know that the function has to look like this f(x)=#. like f(x)=3. and the horizontal line would be at 3. well the derivative of that would be 0. so the graph of the derivative of that function would be nothing. (chap. 3 multiple choice number 4)
the same thing i still don't understand every week. OPTIMIZATION. i hate it. i did learn today though that whenever you optimize a rectangle you will always end up with a square, which means whenever you work it out your x & y should be equal to the same thing. (chap. 3 multiple choice number 3) the x & y both ended up being equal to 11/2.
even though i got b rob to help me today with it, i still cannot do it by myself. any tips? just for optimization in general? please & thank you!
good luck on all of your exams tomorrow everyone :)
ok, ill stop being mean now, and lets talk about calculus. at the study group today, i learned a lot about the process of elimination when it comes to multiple choice questions. also, if there is nothing else you can do with a problem that gives you a function and asks you to find something on a certain interval, like find the absolute extrema on the interval [0,2pi], then you can plug it into your calculator if you absolutely cannot figure it out by hand. also, short cuts are your friend :) like using the table function for problems like these. all of this really helped on the chap. 3 multiple choice part of our study guide.
some things i understand now are how to find a tangent line. the rules of finding a limit approaching infinity. how to take simple derivatives. instantaneous and average speed. all of these things. also how to look a a graph of a function and be able to know what the graph of the derivative of that function will look like, thank you dylan becnel :) haha. i also understand rolle's theorem and mean value theorem very well. what should i explain today? i think i'll explain how to look at the graph of a function and be able to know what the graph of the derivative of that function will look like.
Example:
let's say you are given the graph of a horizontal line. well, you know that the function has to look like this f(x)=#. like f(x)=3. and the horizontal line would be at 3. well the derivative of that would be 0. so the graph of the derivative of that function would be nothing. (chap. 3 multiple choice number 4)
the same thing i still don't understand every week. OPTIMIZATION. i hate it. i did learn today though that whenever you optimize a rectangle you will always end up with a square, which means whenever you work it out your x & y should be equal to the same thing. (chap. 3 multiple choice number 3) the x & y both ended up being equal to 11/2.
even though i got b rob to help me today with it, i still cannot do it by myself. any tips? just for optimization in general? please & thank you!
good luck on all of your exams tomorrow everyone :)
Ash's 8th post
Okay, wow.....Yea
This week: powerpoint presentations and study guides...yipeee...fun *twirls finger nonenthusiastically*
Anyway, I pretty much wore out what I understood, so I can't really explain anything else. Also, I've been studying all weekend and I'm kinda like "duuuuuuuuuhhhhhhh *head hangs to side*" Yea, slightly braindead. Okay, but I will say this
I STILL DON'T GET OPTIMIZATION!!!! -.-
I feel like the stupid little kid that never understands how to spell the word 'cat' with a c not a k.
Also, those packets? I'm about to go cry...if that's what the exam looks like I KNOW I'm going to fail. I get half of it...the other half? Nope. Nada. Zip. Non. Zero.
Also, how is everyone studying for this exam? Doing the packet only? Doing the packet plus staring at your notes for 3 hours ineffectively? Nothing at all? I, for some reason, can't just study by doing the packet problems, or example problems, or just any kind of problems. I also can't study by staring at my notes. I need interaction. Think of me as a 2 year old...I won't get it if I stare at it....I need something to slowly state "That is a bike" over..and over...and over...and over...and over...and over...until I get it! -.-
Okay, I totally did not mean to whine...just merely type..and type..because I'm staring at the laptop screen as questions come to my head.....
*sigh* I guess I have to get off of the computer now and study for Calc, Chemistry, Ap Gov, Western Civ, English, AND the PSAT...by the way
For those of you who are taking the PSAT AND the Calc exam Wed...are you gonna ask your 7th hour teacher to move your exam? Maybe? Yes? No?
Okay..I'm done. I apologize for making you sit here and lose about 45 brain cells.
This week: powerpoint presentations and study guides...yipeee...fun *twirls finger nonenthusiastically*
Anyway, I pretty much wore out what I understood, so I can't really explain anything else. Also, I've been studying all weekend and I'm kinda like "duuuuuuuuuhhhhhhh *head hangs to side*" Yea, slightly braindead. Okay, but I will say this
I STILL DON'T GET OPTIMIZATION!!!! -.-
I feel like the stupid little kid that never understands how to spell the word 'cat' with a c not a k.
Also, those packets? I'm about to go cry...if that's what the exam looks like I KNOW I'm going to fail. I get half of it...the other half? Nope. Nada. Zip. Non. Zero.
Also, how is everyone studying for this exam? Doing the packet only? Doing the packet plus staring at your notes for 3 hours ineffectively? Nothing at all? I, for some reason, can't just study by doing the packet problems, or example problems, or just any kind of problems. I also can't study by staring at my notes. I need interaction. Think of me as a 2 year old...I won't get it if I stare at it....I need something to slowly state "That is a bike" over..and over...and over...and over...and over...and over...until I get it! -.-
Okay, I totally did not mean to whine...just merely type..and type..because I'm staring at the laptop screen as questions come to my head.....
*sigh* I guess I have to get off of the computer now and study for Calc, Chemistry, Ap Gov, Western Civ, English, AND the PSAT...by the way
For those of you who are taking the PSAT AND the Calc exam Wed...are you gonna ask your 7th hour teacher to move your exam? Maybe? Yes? No?
Okay..I'm done. I apologize for making you sit here and lose about 45 brain cells.
Post Number Eight
soooo week number eight has come to a close and calculus still seems to stress me out daily.
oh well :)
This past week we reviewed for our exams and presented our power point presentations. I felt like i learned a lot about different jobs and how much math does play a part in everyday life. But onto the real stuff.
Some things i'm finally catching on to:
oh well :)
This past week we reviewed for our exams and presented our power point presentations. I felt like i learned a lot about different jobs and how much math does play a part in everyday life. But onto the real stuff.
Some things i'm finally catching on to:
- Tangent lines
- Derivatives in general (finallyyyyyyyyy)
- Limits (sometimes)
Of course i'm still not getting some things also:
- Optimization- i understand the steps and all so don't comment me telling me them. I just can't find the two formulas at the beginning. If anyone has any ideas or can help me with this I NEEED IT
- Looking at graphs determining derivatives and such
- Vertical asymptotes
- And of course the easy stuff that i always seem to mess up on that we will not speak of
So now that that was said i'll give an example of something i understand :)
g(x)=x^2 - 4x + 9
Write the equation of the tangent line to the graph of g at x=3.
First you can simply just find the y value so you can later put your information in point slope form. Since you are given the x value at x=3, you just plug it into the original formula to find the y.
g(3)=3^2 - 4(3) + 9
g(3)=6
So your point is (3, 6)
Now you need a slope, so guess what we do now.
Take a derivative, which is what we'll be doing everyday for what feels like the rest of our lives so do ittttt!
g'(x)=2x-4
Now plug in the x value into the derivative.
g'(3)=2(3) - 4
g'(3)=2
Now that you have a point and a slope, you put it into point-slope form because it is asking for an equation of the tangent line.
Your final answer will be y - 6=2(x - 3)
Easy enough, right?
Oh and another thing i learned this week is how to use the table function and that you should treat it like your bible basically (Thanks John!)
If anyone can help me with anything please let me know. I'm always struggling with something. But thanks to all of these study guides i think i'm finally getting a hang of some of these things.
Now for yet another week of Calculus
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