Rolle's Theorem:
1. You have to make sure it is continuous and differentiable on the closed interval [a,b].
2. Plug in your points [a,b] to equation. They have to be equal to continue. If not this theorem cannot be used.
3. Take derivative, solve for x and make sure your values are on the interval.
Example:
f(x)= x^4-2x^2 on [-2,2] find all values c for which f^1(c)=0
1. Is is continuous and differentiable? YES
2. f(-2)=(-2)^4-2(-2)^2=8
f(2)=(2)^4-2(2)^2=8
f(-2)=f(2)=8
3. 4x^3-4x= 0
4x(x^2-1)= 0
x= 0, 1, -1
c= 0, 1, -1
My question is about average speed. What are the steps to solving?
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Average Speed:
ReplyDeleteAn anvil falls off the roof onto Ryan's head. What is its average speed during the first two seconds if y=16t^2 describes the fall.
0: y1=16(0)=0
2:y2=16(2)^2=64 [0,2]
y2-y1 64-0
-------- =m so... m=-------------- =32
x2-x1 2-0
M=32