Question

Verify Rolle’s theorem for the function, f(x) = –1 + cos x in the interval [0, 2π]

Answer 1

For a function f(x)

Continuous in [a, b]

Differentiate in (a, b)

f(a) = f(b)

Then there exist atleast one value of c for which f(x) = 0.

f(0) = –1 + cos (0) = 0

f(2π) = –1 + cos (2π) = 0

f’(x) = – sin x

f’(x) – sin x = 0

x = π

This proves rolle’s theorem.