If f(x) is not differentiable finitely at x = 2 and f(x) + g(x) is differentiable finitely at x = 2 then

JEE Advanced Mathematics question

If is not differentiable finitely at and is differentiable finitely at then

(A) must be differentiable finitely at
(B) must be continuous at
(C) may not be differentiable at
(D) cannot be differentiable at Correct

Answer: (D)

Solution

Suppose were (finitely) differentiable at . Then would be a difference of two functions differentiable at 2, hence differentiable at 2 — contradiction. So cannot be differentiable at : (d). - (a) is the opposite

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Question ID VK-110423