If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function, $f\left(x\right)=9x^4+12x^3-36x^2+25,x\in R,$ then

• A

  $S_1=\left\{-2\right\};S_2=\left\{\mathrm{0,1}\right\}$
• B

  $S_1=\left\{-1\right\};S_2=\left\{\mathrm{0,2}\right\}$
• C

  ${ S}_1=\left\{-\mathrm{2,0}\right\};S_2=\left\{1\right\}$
• Correct answer
  D

  $S_1=\left\{-\mathrm{2,1}\right\};S_2=\left\{0\right\}$

Hence, the correct answer is option: 'D'.