(Solved): The total sales of a company (in millions of dollars) t months from now are given by S(t)=0.02t3+0. ...

The total sales of a company (in millions of dollars) $t$ months from now are given by $S(t)=0.02t^3+0.6t^2+9t+2$. (A) Find $S^{\prime }(t)$. (B) Find $S^{\prime }(4)$ and $S^{\prime }(4)$ (to two decimal places). (C) Interpret $S(9)=146.18$ and $S^{\prime }(9)=24.66$ (A) $S^{\prime }(t)=$ (B) $S(4)=$ $S^{\prime }(4)=$ (C) Choose the correct interpretation of $S(9)=146.18$ A. In approximately 146 months the sales will be increasing by $\$9$ million per month B. In 9 months the sales will be increasing at a rate of $\$146.18$ million per month. C. The total sales 9 months from now will be $\$146.18$ million dollars. D. In approximately 146 months the sales will be $\$9$ million dollars. Choose the correct interpretation of $S^{\prime }(9)=24.66$ A. The total sales 9 months from now will be $\$24.66$ million dollars. B. In 9 months the sales will be increasing at a rate of $\$24.66$ million per month. C. In approximately 25 months the sales will be increasing by $\$9$ million per month D. In approximately 25 months the sales will be $\$9$ million dollars