Q. Let $f,\ g$ and $h$ be real-valued functions defined on the interval [0, 1] by $f(x) = e^{x^{2}} + e^{- x^{2}},\ g(x) = x{e^{x}}^{2}$+${e^{- x}}^{2}$ and$h(x) = x^{2}e^{x^{2}} + e^{- x^{2}}$. If $a,\ b$ and $c$ denote respectively, the absolute maximum of $f,\ g$ and $h$ on [0, 1], then
A) $a = b$ and $c \neq b$
B) $a = c$ and $a \neq b$
C) $a \neq b$ and $c \neq b$
D) $a = b = c$
Explanation
(d)
Given function
$f(x) = e^{x^{2}} + e^{- x^{2}}$
$g(x) = xe^{x2} + {e^{- x}}^{2}$ and
$h(x) = x^{2}e^{x^{2}} + e^{- x^{2}}$ Are strictly increasing on [0, 1]. Hence, at $x = 1$, the given function attains absolute maximum all equal to $e + \frac{1}{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.