For a particular item

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

Problem

For a particular item, total cost and total revenue (in dollars) are modeled by

C(q)=0.005q^{3}+4q+2500 \quad\text{and}\quad R(q)=50q,

where

q

is the number of units produced and sold. Determine the production level

q

(to the nearest whole unit) at which the profit ceases to increase and begins to decrease.