Question

Let f, g and h be real−valued functions defined on the interval [0, 1] by f(x) = e^{x^2} + e^{-x^2}, g(x) = xe^{x^2} + e^{-x^2} and h(x) = x²e^{x^2} + e^{-x^2}. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then 

(A) a = b and c ≠ b

(B) a = c and a ≠ b

(C) a ≠ b and c ≠ b

(D) a = b = c

Answer 1

Answer is (D) a = b = c

a = b = c = e + 1/e ⇒ a = b = c