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Question

The point of inflection for the function f(x)=sin1x is:

A
x=12
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B
x=12
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C
x=12
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D
x=0
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Solution

The correct option is D x=0
Given: f(x)=sin1x
f(x)=11x2=(1x2)1/2
f′′(x)=2x(12)(1x2)3/2
f′′(x)=x(1x2)32
Clearly, the second derivative is zero at x=0 and also it changes sign at x=0. Hence it is a point of inflection.

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