Let for and define

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

f(x)=x^{3}-6x^{2}+9x

for

0\le x\le 4

and define

g(x)=\displaystyle\int_{0}^{x} f(t)\,dt

. Determine all values of

x

(0,4)

at which

g

has a point of inflection, and justify your answer in one or two sentences.