JEE Advanced 2013 Paper 2 Mathematics Q14

Mathematics

Problem

Paragraph for Questions 13 and 14 Let f:[0,1]→Rf:[0,1]\to\mathbb R be a function. Suppose that ff is twice differentiable, f(0)=f(1)=0f(0)=f(1)=0 and f′′(x)−2f′(x)+f(x)≥exf''(x)-2f'(x)+f(x)\ge e^x, x∈[0,1]x\in[0,1]. If the function e−xf(x)e^{-x}f(x) assumes its minimum in the interval [0,1][0,1] at x=1/4x=1/4, which of the following is true?

Browse the problem library