Question

Let f(x) = {(x²|cos(π/x)| : x ≠ 0), (0, : x = 0) then f is

(a) differentiable both at x = 0, x = 2

(b) differentiable at x = 0 but not differentiable at x = 2.

(c) differentiable at x = 2 but not differentiable at x = 0.

(d) neither differentiable at x = 0 nor at x = 2. 

Answer 1

Correct option  (b) differentiable at x = 0 but not differentiable at x = 2.

Explanation:

Thus, f(x) is differentiable at x = 0

At x = 2

Thus, f(x) is differentiable at x = 0 but not differentiable at x = 2.