Answer
$f\left( x \right) = 4{x^3} + {C_1}x + {C_2}$
Work Step by Step
$$\eqalign{
& f''\left( x \right) = 24x \cr
& {\text{Find the general antiderivative }}f'\left( x \right) \cr
& {\text{Using the formulas in Table 2 }}\left( {{\text{see page 358}}} \right) \cr
& {\text{Function: }}cf\left( x \right) \to {\text{Particular antiderivative: }}cF\left( x \right) \cr
& {\text{Function: }}{x^n}\left( {n \ne - 1} \right) \to {\text{Particular antiderivative: }}\frac{{{x^{n + 1}}}}{{n + 1}} \cr
& {\text{we obtain}} \cr
& f'\left( x \right) = 24\left( {\frac{{{x^2}}}{2}} \right) + {C_1} \cr
& f'\left( x \right) = 12{x^2} + {C_1} \cr
& {\text{Find the general antiderivative }}f\left( x \right) \cr
& {\text{Using the formulas in Table 2 }}\left( {{\text{see page 358}}} \right) \cr
& {\text{Function: }}cf\left( x \right) \to {\text{Particular antiderivative: }}cF\left( x \right) \cr
& {\text{Function: }}{x^n}\left( {n \ne - 1} \right) \to {\text{Particular antiderivative: }}\frac{{{x^{n + 1}}}}{{n + 1}} \cr
& {\text{we obtain}} \cr
& f\left( x \right) = 12\left( {\frac{{{x^3}}}{3}} \right) + {C_1}x + {C_2} \cr
& f\left( x \right) = 4{x^3} + {C_1}x + {C_2} \cr} $$
