Explain, in one to two sentences, why a value of for which but cannot correspond to a…

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

Problem

Explain, in one to two sentences, why a value of

t

for which

\dfrac{dx}{dt}=0

but

\dfrac{dy}{dt}\neq 0

cannot correspond to a relative extremum of

y

with respect to

x

for a smooth parametric curve

(x(t),y(t))