Question

Find the value of c(a point where slope of a atangent to curve is zero) if f(x) = Sin(x) is continuous over interval [0,π] and differentiable over interval (0, π) and c ∈(0,π)

(a) π

(b) ^π⁄2

(c) ^π⁄6

(d) ^π⁄4

I had been asked this question in homework.

My question is taken from Rolle’s Theorem topic in section Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (b) ^π⁄2

For explanation I would say: Given, f(x)=Sin(x), x ∈ [0,π].

Now f(0) = f(π) = 0

f’(c) = Cos(c) = 0

 c = ^π⁄2.