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Question

Let h(x)=f(x)a(f(x))2+a(f(x))3
for every real number x.
If f(x) is strictly increasing function, then h(x) is non-monotonic function given

A
a(0,3)
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B
a(2,2)
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C
a(3,)
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D
a(,0)(3,)
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Solution

The correct option is D a(,0)(3,)
h(x)=f(x)a(f(x))2+a(f(x))3
or h(x)=f(x)2af(x)f(x)+3a(f(x))2f(x)
=f(x)[3a(f(x))22af(x)+1]

Now, h(x) is non monotonic function if
3a(f(x))22af(x)+1 changes sign
So,
D>0
4a212a>0
a(,0)(3,)

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