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Question

The interval in which the function x2x2+3 is concave up

A
(1,)
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B
(,1)(1,)
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C
(0,)
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D
(1,1)
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Solution

The correct option is D (1,1)
Given, f(x)=x2x2+3, xR
f(x)=6x(x2+3)2
f′′(x)=18(x2+3)(1x2)(x2+3)4
For concave up, f′′(x)>0
1x2>0
x21<0
x(1,1)

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