Water flows into a reservoir at a rate modeled by cubic meters per hour for

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

Problem

Water flows into a reservoir at a rate modeled by

r(t)=-2t^{2}+12t

cubic meters per hour for

0\le t\le 6

, where

t

is the time in hours since pumping began. Determine the time when the inflow rate is greatest and state that maximum rate, with units.