Consider the curve

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Consider the curve

x=t^{3}+k t,\;y=t^{2}

, where

k

is a constant. (i) Determine

\dfrac{d^{2}y}{dx^{2}}

t=1

in terms of

k

. (ii) For which value of

k

does the curve have an inflection point at

t=1