Mathematics

Problem

For a spherical balloon, the radius

r(t)

is a differentiable function of time. At

t=4\text{ s}

, the balloon reaches a local maximum radius. Which of the following statements best describes the instantaneous rates of change of its volume

V(t)

and surface area

A(t)

at that instant? a)

\displaystyle \frac{dV}{dt}<0\text{ and }\frac{dA}{dt}<0

\displaystyle \frac{dV}{dt}=0\text{ but }\frac{dA}{dt}\neq 0

\displaystyle \frac{dV}{dt}=0\text{ and }\frac{dA}{dt}=0

\displaystyle \frac{dV}{dt}\neq 0\text{ while }\frac{dA}{dt}=0