SOLUTION: Determine whether Rolle's theorem applies to the function shown below on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's theorem. f(x)=x(x-8)^

Question 1155428: Determine whether Rolle's theorem applies to the function shown below on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's theorem.
f(x)=x(x-8)^2; [0,8]
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Rolle's Theorem
Let be differentiable on the open interval (,) and continuous on the closed interval [,].
Then if , then there is one point in (,) where '.

;
[,]=[,]
check if for

=>
then derivate

apply the Product Rule : '='*+* '
'
'
'
'
find point in (,) where '

solutions:
if =>
if =>
the point(s) that are guaranteed to exist by Rolle's theorem are:
(,) and (,)

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