A company determines that monthly sales $S$, in thousands of dollars, after $t$ months of marketing a product is given by $S(t)=2 t^{3}-40 t^{2}+220 t+160$
a) Find $S^{\prime}(1), S^{\prime}(2),$ and $S^{\prime}(4)$
b) Find $S^{\prime \prime}(1), S^{\prime \prime}(2),$ and $S^{\prime \prime}(4)$
c) Interpret the meaning of your answers to parts (a) and (b).