Let , , and be real-valued functions defined on the interval by , , and . If , , and…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

f

g

, and

h

be real-valued functions defined on the interval

[0,1]

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

g(x)=xe^{x^2}+e^{-x^2}

, and

h(x)=x^2e^{x^2}+e^{-x^2}

. If

a

b

, and

c

denote, respectively, the absolute maximum of

f

g

, and

h

[0,1]

, then (1)

a=b

and

c\ne b

(2)

a=c

and

a\ne b

(3)

a\ne b

and

c\ne b

(4)

a=b=c