For a parametric curve ,

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

Problem

For a parametric curve

x=f(t)

y=g(t)

, suppose at

t=t_{0}

we have

f'(t_{0})=0

while

g'(t_{0})\neq0

and the second derivatives exist. Which statement is true about

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

t=t_{0}

? (a)

\dfrac{g''(t_{0})}{g'(t_{0})}

(b) It is not defined because its denominator becomes zero. (c)

-\dfrac{f''(t_{0})}{g'(t_{0})}

(d)

0