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

Correct answer: D. a=b=c Given function, aligned & f(x)=e^ x^2 +e^ -x² , & g(x)=x e^ x^2 +e^ -x² and & h(x)=x² e^ x^2 +e^ -x² are strictly aligned increasing on [0,1] . Hence, at x=1 , the given function attains absolute maximum all equal to e+(1)/(e) . a=b=c

JEE Advanced 2010Paper 1

Exam: JEE Advanced
Year: 2010
Paper: Paper 1
Subject: Mathematics
Chapter: Application of Derivatives

JEE Advanced 2010 · Paper 1 · Mathematics · Application of Derivatives

Let f, g and h be real-valued functions defined on the interval...

Let

f, g

and

h

be real-valued functions defined on the interval

[0,1]

f(x)=e^{x^2}+e^{-x^2}, \quad 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

[0,1]

, then

Options

A $a=b$ and $c \neq b$
B $a=c$ and $a \neq b$
C $a \neq b$ and $c \neq b$
D $a=b=c$

Correct answer

D. $a=b=c$

Step-by-step solution

Given function,

\begin{aligned}& f(x)=e^{x^2}+e^{-x²}, \\ & g(x)=x e^{x^2}+e^{-x²} \text{ and }\\ & h(x)=x² e^{x^2}+e^{-x²} \text{ are } \quad \text{ strictly } \end{aligned}

increasing on

[0,1]

. Hence, at

x=1

, the given function attains absolute maximum all equal to

e+\frac{1}{e}

. \Rightarrow \quad a=b=c

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