Instructions

Let $$f : [0, 1] \rightarrow R$$ (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies $$f"(x) - 2f'(x) + f(x) \geq e^x, x \in [0, 1]$$.

Question 54

If the function $$e^{-x} f(x)$$ assumes its minimum in the interval [0, 1] at $$x = \frac{1}{4}$$ which of the following is true ?

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JEE (Advanced) 2013 Paper-2

If the function $$e^{-x} f(x)$$ assumes its minimum in the interval [0, 1] at $$x = \frac{1}{4}$$ which of the following is true ?

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