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Question

If f(x) is a differentiable function and f(x)x3 is strictly increasing, then f(x)+xx2 is

A
increasing
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B
decreasing
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C
not monotonic
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D
not depends on nature of f(x)
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Solution

The correct option is A increasing
Let H(x)=f(x)x3
H(x)=f(x)3x2>0
f(x)>3x2
Let h(x)=f(x)+xx2
h(x)=f(x)+12x
h(x)>3x22x+1>0
Hence, h(x) is increasing.

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