Soooo...we started off the week doing the same things we did last week, and i still don't all the way understand! But it's getting there i guess. We were still taking the derivatives of the BIG ones, it's just hard to figure out what to do first! Then we started with Arc Sin .. i actually understand a little better now! GO ME! Oh and we had our first TEST Wednesday! Wahoo...yeah that was HARD! it was on verticle asymptotes, horizontal symptotes, limits, points of discontinutity, and all of the derivatives we had learned so far. I studied alot! [even if it didn't pay off]
For verticle asymptotes you set the bottom equal to zero then after canceling you solve! For horizontal asymptotes it must be y = a number. To find it, take the limit of infinity, but remember if you get infity it DOES NOT EXIST! For example:
(x^2 + 4x + 9)
---------------
(4x^2 + x + 6)
since the HIGHEST exponet is the same then you divided the coefficients. Giving you y=one forth!
But, for
(x^3 + x)
----------
x
it's DNE because the greater one is at the top and it's infinity, which means no horizontal asyptotes!
Remember that for limits:
- if the degree at the top is greater there is no hoizontal asymptotes, and it's + or - infinity
- if the degree at the top is less then it's zero
- if the degree at the top and bottom are equal then you divide the leading coefficients to get your answer!
In order to find the limit of a number you can either plug it into the equation or, if you have a graph, just look at the graph!
To find points of discontinutity, always factop the top and bottom, then, if possible, make cancelations. Set the bottom equal to zero. If able to make cancelations, it's a removable ... for fractions, if you can still set the bottom equal to zero, then it's an asymptote, or infinite at that number! However if it's a piecewise then it could be a removable, jump, or it could be contiunuous. Solve by what is given. if it has an equal then it's not a removable. When you solve, if they're not the same it's a jump. But, if you solve and they are equal then it's continuous. Remember: if there's NO equal then it's a removable at that point!
Thursday and Friday we learned about ... increasin, decreasing, positive and negative slopes, concave up or down, horizontal tangents, derivative above the axis, as well as below the axis, what a zero of a derivative means, the max and min, and the points of inflection, knowing that the slope is set equal to zero! ... PHEWW ... you'd think it's hard by the way it sounds...but it's just basic concepts really!
- if the slope is positive it's increasing.
- if the slope is negative it's decreasing.
- above the x axis would be from zero to infinity.
- below the x axis would be from negative infinity to zero.
- if you're concave up then your slpe is positive.
- if you're concave down then your slpe is negative.
- a horizontal tangent is the slope of a horizontal line [which is zero].
- remember that concave up is like a bowl and concave down is like a frown.
- if increasing increasing or decresing decreasing occurs...it's neither the max or the min [just a reminder]
- finding the value of y ... just plug into the original!
We even learned about the first derivative test:
- take the derivative
- set equal to zero
- solve for x [which will give you max and min, hoizontal tangents, extrama..which is critical]
- set up intervals using the last step
- plug in the first derivative equation
- to find an absolute max/min: plug values from the last step into the original function.
- check endpoints
so yeah that's just about all folks!...have a great weekend! [and labor day]...
but...i still don't know what to do first for the BIG deriviatives!... :[
ellie, whenever you are faced with a big derivative, just remember to break it down step by step. Be on the lookout for the product rule and quotient rule first. Then look for the exponent rule and the ln rule or the e^u rule. Just remembering those formulas will help tremendously. That is what i did for the test and it made my life so much easier. And do not forget about u'. That is the most common thing missed when taking derivatives. Just remember, when you take the derivative of something and the u looks like it has another derivative inside, take it again lol. Hope i helped!
ReplyDeleteBig derivatives aren't all that hard. You just need to look at it separately. What I do sometimes when I get confused is just think...okay what am I looking at.
ReplyDeleteWell, if it's a huge fraction, just worry about doing the quotient rule, forget about what is it in for the moment. Whenever you get to those parts of the derivative deal with those separately,forgetting what you had before.
You have to separate your mindset when dealing with really large derivatives...
It also helps if you know them off the back of your hand. Write them out a couple times. Once you completely understand and remember the derivative formulas, the larger derivatives will come easier to you.
okay so with this whole derivative thing, i asked the same question in my blog and everyone says just work it from the outside in so im guessing that would be the way to get it.
ReplyDelete