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Question

Let f, g and h be real-valued functions defined on the interval [0,1] by f(x)=ex2+ex2, g(x)=xex2+ex2 and h(x)=x2ex2+ex2 If a, b and c denote, respectively, the absolute maximum of f, g and h on [0,1] respectively then

A
a=b and cb
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B
a=c and ab
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C
ab and cb
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D
a=b=c
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Solution

The correct option is D a=b=c
1xx2x[0,1]

ex2xex2x2ex2 i.e.

ex2+ex2ex2+xex2ex2+x2ex2
Equality holds when x=1

i.e. f(x)g(x)h(x)xϵ[0,1]

Thus, f(1) is the greatest.

Thus, a=b=c=e+1e

Hence, a=b=c.


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