If S_1 and S_2 are respectively the sets of local minimum

Question:

If $S_{1}$ and $S_{2}$ are respectively the sets of local minimum and local maximum points of the function, $f(\mathrm{x})=9 \mathrm{x}^{4}+12 \mathrm{x}^{3}-36 \mathrm{x}^{2}+25, \mathrm{x} \in \mathrm{R}$, then :

  1. $\mathrm{S}_{1}=\{-2,1\} ; \mathrm{S}_{2}=\{0\}$

  2. $\mathrm{S}_{1}=\{-2,0\} ; \mathrm{S}_{2}=\{1\}$

  3. $\mathrm{S}_{1}=\{-2\} ; \mathrm{S}_{2}=\{0,1\}$

  4. $S_{1}=\{-1\} ; S_{2}=\{0,2\}$

Correct Option: 1

Solution:

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