State the conditions

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

Problem

State the conditions, in terms of

\dfrac{dy}{d\theta}

and

\dfrac{dx}{d\theta}

, that must hold at a point on a polar curve

r=f(\theta)

for the tangent line to be horizontal and for it to be vertical.