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)^
Algebra ->
Test
-> 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)^
Log On
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 (,)
