Answer
$$\eqalign{
& f'\left( s \right) = 96{s^2} - 4.2s + 7{\text{ }} \cr
& f''\left( s \right) = 192s - 4.2 \cr} $$
Work Step by Step
$$\eqalign{
& f\left( s \right) = 32{s^3} - 2.1{s^2} + 7s \cr
& {\text{Differentiate}} \cr
& f'\left( s \right) = \frac{d}{{ds}}\left( {32{s^3}} \right) - \frac{d}{{ds}}\left( {2.1{s^2}} \right) + \frac{d}{{ds}}\left( {7s} \right) \cr
& f'\left( s \right) = 32\frac{d}{{ds}}\left( {{s^3}} \right) - 2.1\frac{d}{{ds}}\left( {{s^2}} \right) + 7\frac{d}{{ds}}\left( s \right) \cr
& {\text{use the power rule}} \cr
& f'\left( s \right) = 32\left( {3{s^2}} \right) - 2.1\left( {2s} \right) + 7\left( 1 \right) \cr
& f'\left( s \right) = 96{s^2} - 4.2s + 7 \cr
& \cr
& {\text{Differentiate to find the second derivative}} \cr
& f''\left( s \right) = \frac{d}{{ds}}\left( {96{s^2}} \right) - \frac{d}{{ds}}\left( {4.2s} \right) + \frac{d}{{ds}}\left( 7 \right) \cr
& f''\left( s \right) = 96\frac{d}{{ds}}\left( {{s^2}} \right) - 4.2\frac{d}{{ds}}\left( s \right) + \frac{d}{{ds}}\left( 7 \right) \cr
& f''\left( s \right) = 96\left( {2s} \right) - 4.2\left( 1 \right) + 0 \cr
& f''\left( s \right) = 192s - 4.2 \cr} $$
