Question

If f(x) = {(- x - π/2 : x ≤ - π/2), (-cosx : - π/2 < x ≤ 0), (x - 1, : 0 < x < 1), (lnx : x > 1) then

(a) f(x) is cont at x = –π/2

(b) f(x) is not differentiable at x = 0

(c) f(x) is differentiable at x = 1

(d) f(x) is differentiable at x = – 3/2

Answer 1

Correct option (a, b, c, d)

Explanation:

We have

Clearly f(x) is continuous at x = π/2 and f(x) is not differentiable at x = 0.

Also, f(x) is differentiable at x = 3/2

Thus, f(x) is differentiable at x = 1.