What is the f(x)=(1/x-4/(x^3))(x^3-5x-1) ?

The f(x)=(1/x-4/(x^3))(x^3-5x-1) is

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f(x)=(1/x-4/(x^3))(x^3-5x-1)

f (x) = (\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1)

Domain : x < 0 or x > 0

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

X Intercepts : (- 2, 0), (2, 0), (- 0.20163 \dots, 0), (- 2.12841 \dots, 0), (2.33005 \dots, 0)

Asymptotes : None

Extreme Points : Minimum (- 2.06329 \dots, - 0.01559 \dots), Maximum (- 0.29789 \dots, 68.50855 \dots), Minimum (2.15833 \dots, - 0.11376 \dots)

Interval Notation

Domain : (- \infty, 0) \cup (0, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

(\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1) : x < 0 or x > 0

Range of

(\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1) : - \infty < f (x) < \infty

Axis interception points of

(\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1) :

X Intercepts

: (- 2, 0), (2, 0), (- 0.20163 \dots, 0), (- 2.12841 \dots, 0), (2.33005 \dots, 0)

Asymptotes of

(\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1) :

None

Extreme Points of

(\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1) :

Minimum

(- 2.06329 \dots, - 0.01559 \dots),

Maximum

(- 0.29789 \dots, 68.50855 \dots),

Minimum

(2.15833 \dots, - 0.11376 \dots)

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