Answer
$$f'\left( 3 \right) = - 39$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \frac{{{x^3}}}{9} - 7{x^2} \cr
& {\text{Find the derivative of }}f\left( x \right), \cr
& f'\left( x \right) = {D_x}\left( {\frac{{{x^3}}}{9} - 7{x^2}} \right) \cr
& {\text{use sum rule for derivatives}} \cr
& f'\left( x \right) = {D_x}\left( {\frac{{{x^3}}}{9}} \right) - {D_x}\left( {7{x^2}} \right) \cr
& {\text{constant multiple rule}} \cr
& f'\left( x \right) = \frac{1}{9}{D_x}\left( {{x^3}} \right) - 7{D_x}\left( {{x^2}} \right) \cr
& {\text{solve derivatives}} \cr
& f'\left( x \right) = \frac{1}{9}\left( {3{x^2}} \right) - 7\left( {2x} \right) \cr
& f'\left( x \right) = \frac{1}{3}{x^2} - 14x \cr
& \cr
& {\text{evaluate }}f'\left( 3 \right) \cr
& f'\left( 3 \right) = \frac{1}{3}{\left( 3 \right)^2} - 14\left( 3 \right) \cr
& {\text{simplifying}} \cr
& f'\left( 3 \right) = - 39 \cr} $$
