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Question

Which one of the following option is always correct for x>0

A
ex1+x
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B
ex<1+x
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C
ex1+x
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D
ex>1+x
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Solution

The correct option is D ex>1+x
Let f(x)=ex1x
Now for critical points, f(x)=ex1=0x=0
For x>0; f(x)>0 i.e. strictly increasing and
For x<0; f(x)<0 i.e. strictly decreasing
So, f(x)>f(0) for x>0
ex1x>110
ex>1+x

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