Question

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

• A. $S_1 = \{ -2, 1\} ; S_2 = \{0 \}$
• B. $S_1 = \{ -2, 0\} ; S_2 = \{1 \}$
• C. $S_1 = \{ -2\} ; S_2 = \{0 , 1 \}$
• D. $S_1 = \{ -1\} ; S_2 = \{0 , 2 \}$

Answer 1

Answer: (A)

$f\left(x\right) =9x^{4} +12x^{3} -36x^{2} +25 $
$ f'\left(x\right) =36x^{3} + 36x^{2} -72x $
$ =36x\left(x^{2}+x-2\right) $
$ =36x\left(x-1\right)\left(x+2\right) $
Points of minima = {-2, 1} = $S_1$
Point of maxima = {0} = $S_2$