Mathematics

Problem

t=2

, a particle moving along a parametric path has

\dfrac{dx}{dt}=5

and

\dfrac{d}{dt}\!\left(\dfrac{dy}{dx}\right)=-3

. Indicate whether the curve is concave up or concave down with respect to the

x

–axis at this instant, and justify your answer using the sign of

\displaystyle \frac{d^{2}y}{dx^{2}}