Well we have now gone straight ap practice tests. This is making me nervous! I'm forgetting some easy stuff and making stupid mistakes. There are a few things though that I am actually remembering and learning while correcting these tests:
1. The derivative of e^u is simply (e^u)u^1. I don't know why I always forget that.
2. Average value means take the integral.
Example: The average value of f(x)= -1/x^2 on [1/2, 1].
1/b-a 1S1/2 (-1/x^2)
1/(1-1/2)S x^-2
2[(-x^-1)/-1] = 2/x still have to integrate from 1/2 to 1
(2/1)-(2/(1/2) = -2
3. Approximate=linearization
Example: If f(1)=2 and f^1(1)=5, use the equation of the line tangent to the graph of f at x=1 to approximate f(1.2).
All you do is put it in to point slope form and solve
y-2=5(x-1)
y-2=5(1.2-1)
y-2=5(.2)
y=1+2= 3
4. Make sure to read the problem carefully because half the time you can eliminate at least two answer choices.
5. And finally use your calculator for the calculator section! It sounds dumb, but we all don't. Always try to graph the equation given or use the table and your calculator can take derivatives and integrals.
My question is about this formula H^1(x)=1/f^1(H(x)). I put a star by this formula in my notes, but I can't tell what kind of problems it is used for. Can anyone help with that?
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The equation you are referring to is used in the following problem...
ReplyDeleteThe function f(x) = x^5 + 3x - 2 passes through the point (1,2). Let f^-1 denote the inverse function. What does (f^-1)'(2) equal?
So basically its used when you are asked the find the derivative of an inverse function at some x value. To do this you use your formula
1
----
f'(f^-1(x))
So, f^-1(2) = 1 because for inverse functions you switch the domain and range--or the x and y's.
Now you have
1
---
f'(1)
Well that's simple. Take the derivative of your function to get 5x^4+3. Now plug in 1 to get 8.
So the final answer is 1/8.
Hope this helps.
for this problem, all you have to do is figure out what it's asking for and then solve it by the chain rule..i can explain it to you more in depth at school, because once i learned..it's really easy!
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