MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Ilya decorates small cakes in his bakery. The time it takes him to decorate x cakes is modelled by T(x)=0.003x3+10x+200 minutes.
(1) If Ilya wants to work at most 12 hours in a day, what is the largest number of cakes he can decorate?
(2) Ilya can choose to decorate between 20 and 40 cakes per day, inclusive. Find the minimum and maximum time he can take per cake on average.