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Question: The inflection points on the graph of function y = \(\int_{0}^{x}{(t - 1)(t - 2)^{2}dt}\) are...

The inflection points on the graph of function

y = ∫0x(t−1)(t−2)2dt\int_{0}^{x}{(t - 1)(t - 2)^{2}dt} are

A

x = –1

B

x = 3/2

C

x = 4/3

D

x =1

Answer

x = 4/3

Explanation

Solution

dydx\frac{dy}{dx}= (x – 1)(x – 2)2 so d2ydx2\frac{d^{2}y}{dx^{2}}= (x – 2) × (3x – 4).

The points of inflection are given by d2ydx2\frac{d^{2}y}{dx^{2}} = 0

So x = 2, x = 4/3 are points of inflection.