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

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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.

asked Jan 23, 2015 in CALCULUS by anonymous

1 Answer

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Step1:

The function image

image

Rolle's theorem:

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

image

image

image

image

image

Rolle's theorem is applicable.

Step 2:

image

Differentiating with respect to image.

Apply Quotient rule in derivatives .

image

image

image

image

Step 3:

image

image

Solve the equation image.

Compare it to  image

image

Roots are image.

image

image

image

image

image is on image.

Solution:

image.

answered Jan 23, 2015 by david Expert

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