Let f(x) = x|x| and g(x) = x. Statement-1 : gof is differentiable at x = 0 and its derivative is continuous at that point. Statement-2 : gof is twice differentiable at x = 0.

JEE Main 2009 Mathematics question

Let and . Statement-1 : gof is differentiable at and its derivative is continuous at that point. Statement-2 : gof is twice differentiable at .

(1)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(2)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(3)Statement-1 is true, Statement-2 is falseCorrect
(4)Statement-1 is false, Statement-2 is true

Answer: (3)

, with derivative , which exists and is continuous at 0 (value 0) — Statement 1 is true. The second derivative at 0

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Question ID VK-039189