The profit of a company can be modelled by the polynomial function p(t)=-t^3+12t^2-21t+10. When will the company make their maximum profit of $108000?

Question

Im not sure how to solve this. Please help

Answer 1

p(t)=-t^3+12t^2-21t+10

p'(t)=-3t²+24t-21=0, if t=1, or t=7, p(1)=0, p(7)=108.

So, the maximum profit can be made after 7 t time periods.