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Question

The point of inflection of the function y=x0(t23t+2)dt is :

A
(32,34)
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B
(32,34)
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C
(12,32)
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D
(12,32)
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Solution

The correct option is A (32,34)
Given
y=x0(t23t+2)dt....(i)
On differentiating w.r.t x, we get
dydx=x23x+2.....(ii)
Again on differentiating w.r.t x we get
d2ydx2=2x3....(iii)
We know that, at point of inflection
d2ydx2=0
From Eq(iii) we get
2x3=0x=32
Now, we have to check behaviour of d2ydx2 at point x=32
Clearly at x=32 sign at d2ydx2 changes
(32,34) is point of inflection.

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