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Popular >

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

Solution

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

Solution

Domain : x < 0 or x > 0

Range : f (x) > (- \infty)^{\frac{5}{3}}

X Intercepts : (0.75487 \dots, 0)

Asymptotes : Vertical x = 0

Extreme Points : Minimum (- \frac{1}{4 ^{\frac{1}{5}}}, (1 + \frac{1}{4 ^{\frac{4}{5}}} + 4^{\frac{1}{5}})^{\frac{5}{3}}), Saddle (0.75487 \dots, 0.00000 \dots)

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Interval Notation

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

Range : ((- \infty)^{\frac{5}{3}}, \infty)

Solution steps

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

: (0.75487 \dots, 0)

Asymptotes of

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

Vertical

: x = 0

Extreme Points of

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

Minimum

(- \frac{1}{4 ^{\frac{1}{5}}}, (1 + \frac{1}{4 ^{\frac{4}{5}}} + 4^{\frac{1}{5}})^{\frac{5}{3}}),

Saddle

(0.75487 \dots, 0.00000 \dots)

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Frequently Asked Questions (FAQ)

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