Question

Let h(x) = f₁(x) + f₂(x) + f₃(x) + ....+ f_n(x) where f₁(x), f₂(x), f₃(x), ...., f_n(x) are real valued functions of x.

Statement-1 : f(x) = |cos|x|| + cos^-1(sgnx) + |lnx|  is not differentiable at 3 points in (0, 2n) because

Statement-2: Exactly one function f(x), i = 1, 2, ....., n not differentiable and the rest of the function differentiable at x = a makes h(x) not differentiable at x = a.

(A ) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

(C) Statement-1 is true, statement-2 is false.

(D) Statement-1 is false, statement-2 is true. 

Answer 1

Answer is (A)

y = |ln x| not differentiable at x = 1

y = |cos|x|| is not differentiable at x = π/2, 3π/2

y = cos-1(sgnx) = cos-1(1) = 0 differentible ∀ x ∈ (0, 2π)]