What is the f(x)=(-x(x+4))/((x^2-x-2)^2) ?

The f(x)=(-x(x+4))/((x^2-x-2)^2) is

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f(x)=(-x(x+4))/((x^2-x-2)^2)

f (x) = \frac{- x ( x + 4 )}{( x ^{2} - x - 2 ) ^{2}}

Domain : x < - 1 or - 1 < x < 2 or x > 2

X Intercepts : (0, 0), (- 4, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = - 1, x = 2, Horizontal y = 0

Extreme Points : Minimum (- 6.10724 \dots, - 0.00750 \dots)

Interval Notation

Domain : (- \infty, - 1) \cup (- 1, 2) \cup (2, \infty)

Solution steps

Domain of

\frac{- x ( x + 4 )}{( x ^{2} - x - 2 ) ^{2}} : x < - 1 or - 1 < x < 2 or x > 2

Axis interception points of

\frac{- x ( x + 4 )}{( x ^{2} - x - 2 ) ^{2}} :

X Intercepts

: (0, 0), (- 4, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{- x ( x + 4 )}{( x ^{2} - x - 2 ) ^{2}} :

Vertical

: x = - 1, x = 2,

Horizontal

: y = 0

Extreme Points of

\frac{- x ( x + 4 )}{( x ^{2} - x - 2 ) ^{2}} :

Minimum

(- 6.10724 \dots, - 0.00750 \dots)

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