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Question


The intervals of concavity and convexity of f(x)=ex2 are

A
Convex : (,22)(22,)
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B
Concave:(22,22)
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C
Concave : (,22)(22,)
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D
Convex:(22,22)
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Solution

The correct option is B Concave:(22,22)
f(x)=ex2
f(x)=2xex2
f′′(x)=2ex22xex2(2x)f′′(x)=2ex2(2x21)
f′′(x)>0 convex and f′′(x)<0 concave
So, convex in x(,22)(22,)
Concave in x(22,22)

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