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Popular >

f(x)=(x^2(x+1)^5)/((x-1)^4)

Solution

f (x) = \frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}}

Solution

Domain : x < 1 or x > 1

Range : - \infty < f (x) < \infty

X Intercepts : (0, 0), (- 1, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = 1

Extreme Points : Saddle (- 1, 0), Maximum (\frac{9 - 105}{6}, \frac{316656000 - 30902400 105}{36 ( 3 - 105 ) ^{4}}), Minimum (0, 0), Minimum (\frac{9 + 105}{6}, \frac{316656000 + 30902400 105}{36 ( 3 + 105 ) ^{4}})

+1

Interval Notation

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

Range : (- \infty, \infty)

Solution steps

Domain of

\frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}} : x < 1 or x > 1

Range of

\frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}} : - \infty < f (x) < \infty

Axis interception points of

\frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}} :

X Intercepts

: (0, 0), (- 1, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}} :

Vertical

: x = 1

Extreme Points of

\frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}} :

Saddle

(- 1, 0),

Maximum

(\frac{9 - 105}{6}, \frac{316656000 - 30902400 105}{36 ( 3 - 105 ) ^{4}}),

Minimum

(0, 0),

Minimum

(\frac{9 + 105}{6}, \frac{316656000 + 30902400 105}{36 ( 3 + 105 ) ^{4}})

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Frequently Asked Questions (FAQ)

What is the f(x)=(x^2(x+1)^5)/((x-1)^4) ?
The f(x)=(x^2(x+1)^5)/((x-1)^4) is