Question

Let f(x) = x|x|, g(x) = sin x and h(x)=(gof)(x). Then

(A) h(x) is not differentiable at x = 0.

(B) h(x) is differentiable at x = 0, but h’(x) is not continuous at x = 0.

(C) h’(x) is continuous at x = 0 but it is not differentiable at x = 0. 

(D) h’(x) is differentiable at x = 0.

Answer 1

Answer is (C) h’(x) is continuous at x = 0 but it is not differentiable at x = 0.

LHD = -2

RHD = 2

Therefore, h′(x) is continuous at x = 0 but is not differentiable at x = 0.