For a parametric curve

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

Problem

x=f(t),\,y=g(t)

, it is known that at

t=t_0

the derivatives satisfy

f'(t_0)>0,\; g''(t_0)=0

, and

g'(t_0)f''(t_0)<0

. Without performing any explicit differentiation, determine the sign (positive, negative or zero) of

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

t=t_0

, giving a brief reason.