Let the function f(x) be defined as below. f(x) = cases ^ -1 + x^2, & 0 < x < 1 2x, & x 1 cases f(x) can have a minimum at x = 1 if the value of is

JEE Advanced Mathematics question

Let the function be defined as below.

f(x) =

can have a minimum at if the value of is

Answer: (A)

. For a (local) minimum at we need for all near 1. - **Right of 1:** for . This side is always fine. - **Left of 1:** as . - If , i.e. , then

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Question ID VK-109408