The curve defined for by and has several candidate values of where

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The curve defined for

-2\le t\le 2

x=t^{3}-t

and

y=t^{5}-5t

has several candidate values of

t

where

\frac{d^{2}y}{dx^{2}}=0

. Identify each value of

t

in this interval at which the curve actually possesses an inflection point and give the corresponding coordinates.