The family of curves is given by and

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

Problem

The family of curves is given by

x = t

and

y = t^{3} + k t

, where

k

is a real constant. Find the value of

t

(in terms of

k

if necessary) at which an inflection point occurs, and state whether this value depends on

k