9.5.89: The total sales of a company​ (in millions of​ dollars) t months from now are given by S(t)=0.04t^3+0.8t^2+8t+7.

Question

The total sales of a company​ (in millions of​ dollars) t months from now are given by S(t)=0.04t^3+0.8t^2+8t+7.

​(A) Find S′(t).

​(B) Find ​S(6​) and S′(6) ​(to two decimal​ places).

​(C) Interpret ​S(11​)=245.04 and S′(11)=40.12.

Answer 1

The total sales of a company​ (in millions of​ dollars) t months from now are given by S(t)=0.04t^3+0.8t^2+8t+7.

​(A) Find S′(t).

S'(t) = 0.12t² + 1,6t + 8

​(B) Find ​S(6​) and S′(6) ​(to two decimal​ places).

S(6) = $ 92.44 million

S'(6) = $21.92 per month slope or rate of increase

​(C) Interpret ​S(11​)=245.04 and S′(11)=40.12.

When the monthly Sales = $245.04, the monthly rate of change is increasing 40.12 million dollars per month