The intervals of concavity and convexity of f(x)=e−x2 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)=e−x2 f′(x)=−2xe−x2 f′′(x)=−2e−x2−2xe−x2(−2x)f′′(x)=2e−x2(2x2−1) f′′(x)>0⇒ convex and f′′(x)<0⇒ concave
So, convex in x∈(−∞,−√22)∪(√22,∞)
Concave in x∈(−√22,√22)