Question

f(x) = 3Sin(2x), is continuous over interval [0,π] and differentiable over interval (0,π) and c ∈(0,π)

(a) π

(b) ^π⁄2

(c) ^π⁄4

(d) ^π⁄8

I had been asked this question during an internship interview.

Asked question is from Rolle’s Theorem topic in division Differential Calculus of Engineering Mathematics

Answer 1

The correct option is (b) ^π⁄2

For explanation: f(x) = 3Sin(2x)

f(0)=0

f(π)=0

Hence,

f’(c) = 6Cos(2c) = 0

c= ^π⁄2.