A polar curve satisfies and for

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

Problem

A polar curve satisfies

\dfrac{dy}{dx}=\theta^{2}

and

\dfrac{dx}{d\theta}=\theta

for

\theta>0

. What is

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

\theta=2

? (a)

8

(b)

4

(c)

2

(d)

12