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}

Answer 1

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Given function :

y = f (x) = 9x⁴ + 12x³ - 36x² + 25

$\frac{dy}{dx} = 36x {}^{3} + 36x {}^{2} - 72x$

$\frac{dy}{dx} = 36x( x{}^{2} + x - 2)$

for maxima or minima

put dy/dx= 0

↪ 36x (x² +x-2) = 0

36x ( x-1) (x+2) = 0

x = 1 , -2 ,0

use sin method ,

observation :

1) dy/dx change it sign from negative to positive at x =-2 and 1 ,

so x= -2 ,1 are the points of local minima.

2) dy/dx changes it sign from positive to negative at x= 0,

so x = 0 is point of local maxima.

therefore,

S₁ = {-2,1}

S₂ = {0}

correct option

a) S₁, {-2, 1} ;S₂ = {0}

Answer 2

Step-by-step explanation:

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}

hope this helps you

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