Let f : R R be a continuous function defined by f(x) = 1 e^x + 2e^ -x . Statement-1: f(c) = 13, for some c R. Statement-2: 0 < f(x) 1 2 2 , for all x R

JEE Main 2010 Mathematics question

Let be a continuous function defined by . Statement-1: , for some . Statement-2: , for all

(1)Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1
(2)Statement-1 is true, Statement-2 is false
(3)Statement-1 is false, Statement-2 is true
(4)Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1Correct

Answer: (4)

By AM–GM, , so , with the maximum attained and as — Statement 2 true. Since f is continuous and $13

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Question ID VK-039278