The depth of water in a pond is modeled by a differentiable function (in meters) for

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

Problem

The depth of water in a pond is modeled by a differentiable function

D(t)

(in meters) for

0\le t\le10

, where

t

is measured in hours. The derivative satisfies

D'(t)>0

for

0<t<4

D'(4)=0

, and

D'(t)<0

for

4<t<10

. Explain what happens to the water level at

t=4

hours and classify this time as a local maximum, a local minimum, or neither.