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Popular >

f(x)=(x^3-3x)(x^2+5)

Solution

f (x) = (x^{3} - 3 x) (x^{2} + 5)

Solution

Domain : - \infty < x < \infty

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

X Intercepts : (0, 0), (- 3, 0), (3, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum - \frac{- 3 + 2 21}{5}, \frac{( - 22 - 2 21 ) ( - 3 + 2 21 ) ^{\frac{3}{2}}}{25 5} + \frac{3 ( - 3 + 2 21 ) - 3 + 2 21}{5 5} + 35 221 - 3, Minimum \frac{- 3 + 2 21}{5}, \frac{( 22 + 2 21 ) ( - 3 + 2 21 ) ^{\frac{3}{2}}}{25 5} - \frac{3 ( - 3 + 2 21 ) - 3 + 2 21}{5 5} - 35 221 - 3

+1

Interval Notation

Domain : (- \infty, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

(x^{3} - 3 x) (x^{2} + 5) : - \infty < x < \infty

Range of

(x^{3} - 3 x) (x^{2} + 5) : - \infty < f (x) < \infty

Axis interception points of

(x^{3} - 3 x) (x^{2} + 5) :

X Intercepts

: (0, 0), (- 3, 0), (3, 0),

Y Intercepts

: (0, 0)

Asymptotes of

(x^{3} - 3 x) (x^{2} + 5) :

None

Extreme Points of

(x^{3} - 3 x) (x^{2} + 5) :

Maximum

- \frac{- 3 + 2 21}{5}, \frac{( - 22 - 2 21 ) ( - 3 + 2 21 ) ^{\frac{3}{2}}}{25 5} + \frac{3 ( - 3 + 2 21 ) - 3 + 2 21}{5 5} + 35 221 - 3,

Minimum

\frac{- 3 + 2 21}{5}, \frac{( 22 + 2 21 ) ( - 3 + 2 21 ) ^{\frac{3}{2}}}{25 5} - \frac{3 ( - 3 + 2 21 ) - 3 + 2 21}{5 5} - 35 221 - 3

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Frequently Asked Questions (FAQ)

What is the f(x)=(x^3-3x)(x^2+5) ?
The f(x)=(x^3-3x)(x^2+5) is