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Question

The minimum value of ex2-1 is


A

1

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B

0

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C

2

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D

None of these.

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Solution

The correct option is B

0


Find the minimum value of the given function

Given : f(x)=ex2-1

Differentiate the function with respect to x,

f'(x)=(x)ex2ex2-1ddxxn=n.xn-1,ddxey=eydydx

We can see that,

f'(x)>0 if x>0.

f'(x)<0 if x<0.

Therefore at x=0 function have minimum value.

Now, evaluate the minimum value of the function

f(x)min=e02-1f(x)min=1-1f(x)min=0

Therefore, the minimum value of the function is 0.

Hence option B is the correct answer.


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