If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x4 + 12x3 - 36x2 + 25, x ∈ R, then :

Question

If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x4 + 12x3 - 36x2 + 25, x ∈ R, then : (A) S1 = -2, 1 ; S2 = 0  (B) S1 = -2, 0 ; S2 = 1  (C) S1 = -2 ; S2 = 0 , 1  (D) S1 = -1 ; S2 = 0 , 2

Tardigrade Admin · Accepted Answer

f(x) =9x4 +12x3 -36x2 +25 f'(x) =36x3 + 36x2 -72x =36x(x2+x-2) =36x(x-1)(x+2) Points of minima = -2, 1 = S1 Point of maxima = 0 = S2

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

$S_{1} = {- 2, 1}; S_{2} = {0}$

$S_{1} = {- 2, 0}; S_{2} = {1}$

$S_{1} = {- 2}; S_{2} = {0, 1}$

$S_{1} = {- 1}; S_{2} = {0, 2}$

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

Q. If S1​ and S2​ are respectively the sets of local minimum and local maximum points of the function, f(x)=9x4+12x3−36x2+25,x∈R, then :

S1​={−2,1};S2​={0}

S1​={−2,0};S2​={1}

S1​={−2};S2​={0,1}

S1​={−1};S2​={0,2}