Which one of the following option is always correct for x>0
A
ex≤1+x
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B
ex<1+x
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C
ex≥1+x
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D
ex>1+x
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Solution
The correct option is Dex>1+x Let f(x)=ex−1−x
Now for critical points, f′(x)=ex−1=0⇒x=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 ⇒ex−1−x>1−1−0 ⇒ex>1+x