If Rolle' s Theorem can be applied, find all values of c in the open interval (a, b) such that f ' (c) = 0.

Question

Determine whether Rolle' s Theorem can be applied to f on the closed interval [a, b]. If Rolle' s Theorem can be applied, find all values of c in the open interval (a, b) such that f ' (c) = 0. if Rolle' s Theorem cannot be applied, explain why not.

Answer 1

Step1:

The function

Rolle's theorem:

If a real valued function f is continuous on a closed interval ,differentiable on the open interval , and , then there exist in the open interval such that .

Rolle's theorem is applicable.

Step 2:

Differentiating with respect to .

Apply Quotient rule in derivatives .

Step 3:

Solve the equation .

Compare it to 

Roots are .

is on .

Solution:

.