Consider the parametric curve and for

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

Problem

Consider the parametric curve

x(t)=t

and

y(t)=t^{3}-6t^{2}+9t

for

0\le t\le5

. Find all values of

t

in this interval at which

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