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