If f(x) = (ab - b^2 - 2)x + _0^x ( ^4 + ^4 ) ,d is a decreasing function of x for all x R and b R, b being independent of x, then

JEE Advanced Mathematics question

If is a decreasing function of for all and , being independent of , then

Answer: (D)

By the Fundamental Theorem of Calculus,

f'(x) = ab - - 2 + x + x .

Now , which takes all values in . Hence

f'(x) = (ab - - 1) - 12 2x .

For to be decreasing for all

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Question ID VK-109427