For a spherical balloon

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For a spherical balloon, the radius r(t)r(t) is a differentiable function of time. At t=4 st=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)V(t) and surface area A(t)A(t) at that instant? (a) dVdt<0 and dAdt<0\displaystyle \frac{dV}{dt}<0\text{ and }\frac{dA}{dt}<0 (b) dVdt=0 but dAdt≠0\displaystyle \frac{dV}{dt}=0\text{ but }\frac{dA}{dt}\neq 0 (c) dVdt=0 and dAdt=0\displaystyle \frac{dV}{dt}=0\text{ and }\frac{dA}{dt}=0 (d) dVdt≠0 while dAdt=0\displaystyle \frac{dV}{dt}\neq 0\text{ while }\frac{dA}{dt}=0

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