A sphere of ice has radius cm that is differentiable with respect to time (in minutes)

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A sphere of ice has radius

r(t)

cm that is differentiable with respect to time

t

(in minutes). Explain briefly why a negative value of

r'(t)

at some instant must imply that the volume

V(t)

of the sphere is decreasing at that same instant.