Explain why confirming a change in the sign of on either side of a candidate…

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

Problem

Explain why confirming a change in the sign of

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

on either side of a candidate parameter value

t=c

is necessary before declaring the corresponding point on a parametric curve to be an inflection point.