Let f : [1, ) [2, ) be a differentiable function such that f(1) = 2. If 6 _1^x f(t) ,dt = 3x ,f(x) - x^3 for all x 1, then the value of f(2) is

JEE Advanced 2011 Mathematics question

Let be a differentiable function such that . If

6 f(t) dt = 3x f(x) -

for all , then the value of f(2) is

Answer: 6

Solution

Status: BONUS / MARKS TO ALL. Mathematical status: the given conditions are inconsistent, so no function satisfies all of them. Putting x = 1 in the integral equation gives , which contradicts the stated ;

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Question ID VK-025940