For the function  $f\left(x\right)=2x^3-3x^2-72x+12$ . Choose the correct options from below

For     $\max /\min \frac{df\left(x\right)}{dx}=0$
 $$\begin{gathered} 6x^2+6x-72=0 \\ 6(x^2-x-12)=0 \\ {x}^2-x-12=0 \\ {x}^2-4x+3x-12=0 \\ x(x-4)+3(x-4)=0 \\ (x-4)(x+3)=0 \\ x=4,-3 \\ \frac{d^{2}f\left(x\right)}{d{x}^2}=2x-1 \\ 2\left(4\right)-1 2(-3)-1 \\ 7(+ve) -7(-ve) \\ min max \end{gathered}$$