So, school tomorrow! Yay? No.
I hate mornings. -.-
These holidays were relatively productive ^^ I lie. I got nothing accomplished except eating, showering, procrastinating, and sleeping. Oh, and finding my aquarium shrimp I have been looking for, but that's not mathy.
But anyway, on to math.
This isn't relating to something that I learned this year in Calc, yet, but I want to talk about it anyway. (since it mayyy ;] come in handy for an upcoming project)
The Spiral of Archimedes! I learned about this in Math Circle during the summer (totally fun, must re-apply this year). This Spiral, I don't remember what's so amazing about it, but it occurs naturally!! look at sunflower seeds while they are still in the plant, the pattern they make is the Spiral of Archimedes! A Nautilus Shell also is in the shape of the Spiral of Archimedes! Today, this spiral is used in building roller coasters! This could be useful for our future projects...
Anyway, that was my random bit of math for the day!
Now, I want to review something that we actually learned in Calc. Hmm....what can I do that no one hasn't exhausted already? Nothing =/
But I'll do.....IMPLICIT DERIVATIVES!
So, you know what a derivative is, right? *random mumbling is heard* THAT'S RIGHT!
So, implicit derivatives are just that but solving for dy/y'!
Example!
3x^2 + 2y = 0
1. 6x dx/dx + 2dy/dx = 0
2. 2dy/dx = -6x
3. dy/dx = -3x!
(I think...my mind's trying to fall into denial about school tomorrow)
That IS right, isn't it?
As for what I STILL don't get:
Optimization! I'm failing..miserably
I half-way understand washers/disks..I'm not sure what I'm confused about though...
I wish everyone luck in school tomorrow!!
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Optimization is pretty easy when everything's given to you in the problem. In the problem, you will be given two equations and you are asked to maximize or minimuze one of them. The one you are asked to maximize or minimize will be your primary equasion. Your secondary will most likely be set equal to a number. These are the steps:
ReplyDelete1. Locate the primary and secondary equasions
2. Solve the secondary for one variable
3. Plug into primary
4. Take the derivative and solve (yielding one of your answers)
5. Plug back into your secondary equation to get your second answer
*Usually in optimization equations they are asking for more than one answer. For example, if they are asking to maximize an area, they will most likely ask to find the perimiter of an object, yielding more than one answer.
I will try to explain this the best i can. First you identify the primary and secondary equations in the problem. You then solve the secondary equation for a variable and plug that variable into the primary equation. After that, you will take the derivative of the primary and solve for x. Then plug the x value back into the secondary equation to get another value. Those two values will be your answers.. Hope this helps ash!
ReplyDeleteheres the steps
ReplyDelete1. Locate the primary and secondary equations
2. Solve the secondary equation for one variable
3. Plug into primary
4. Take the derivative and solve which will givce you on of your ansewrsw
5. Plug back into your secondary equation to get your second answer
HI YAAAAAAAAA
ok so you are given two equations in the problem, you figure out which one is your primary and which one is your seconday equation! step 1
ReplyDeletestep 2 is to solve the secondary equation for one variable, it doesn't matter which variable it is.
step 3 is to plug in your secondary equation solved for one variable(step2) into your primary equation.
step 4 is take the derivative of that (step3) and solve. which gives you one answer
step 5 plug that(step4) back into secondary equation and get second answer.
also for disks and washers, remember they both have volume and area formulas. which are the same, except volume is squared while area is not.
first: set up primary and secondary equeations.
ReplyDeletesecond: solve secondary for a variable.
Third: plug it back into the primary take derivative.
Fourth: solve for the variable.
Fifth : plug back into your secondary and solve for remainding variable.