If the function f(x) = cases -x, & x<1 a+ ^ -1 (x+b), & 1 x 2 cases is differentiable at x = 1, then ab is equal to

JEE Main 2016 Mathematics question

If the function is differentiable at , then is equal to

(1)Correct
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Answer: (1)

Solution

Differentiability at requires both continuity and equality of the one-sided derivatives. **Derivatives:** from the left, . From the right, , which at is . Equating,

= 1 \

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Question ID VK-115574