## Some questions based on Rolle’s theorem

Problem 1:

Verify the truth of Rolle’s theorm for the following functions:

(a) on the interval .

(b) on the interval .

(c) on the interval .

(d) on the interval .

Problem 2:

The function has roots 1 and . Find the root of the derivative mentioned in Rolle’s theorem.

Problem 3:

Verify that between the roots of the function lies the root of its derivative.

Problem 4:

Verify the truth of Rolle’s theorem for the function on the interval .

Problem 5:

The function becomes zero at the end points of the interval . Make it clear that the derivative of the function does not vanish anywhere in the interval . Explain why Rolle’s theorem is NOT applicable here.

Calculus is the fountainhead of many many ideas in mathematics and hence, technology. Expect more beautiful questions on Calculus !

-Nalin Pithwa

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