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Question

The function f(x)=1ex22


A

Decreasing for all x

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B

Increasing for all x

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C

Decreasing for x<0 and increasing for x>0

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D

Increasing for x<0 and decreasing for x>0

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Solution

The correct option is C

Decreasing for x<0 and increasing for x>0


Explanation for correct option

Given function, f(x)=1ex22

So, f'(x)=d1-ex22dx

=ex22dx22dx[dexdx=ex and applying chain rule]

=xex22

The critical point of f(x) are the values of x for which f'(x)=0.
Thus, f'(x)=0 when x=0

So, x=0 is the only critical point.

Also, f'(x)=xex22<0 when x<0. Thus, f(x) decreases in this interval.

And, f'(x)=xex22>0 when x>0. Thus, f(x) increases in this interval.

Hence, the correct option is C.


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