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Popular Functions >

y= 1/2 (x^3-4x)^{3/2}

Solution

y = \frac{1}{2} (x^{3} - 4 x)^{\frac{3}{2}}

Solution

Domain : - 2 \leq x \leq 0 or x \geq 2

Range : f (x) \geq 0

X Intercepts : (0, 0), (- 2, 0), (2, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (- 2, 0), Maximum (- \frac{2}{3 ^{\frac{1}{2}}}, \frac{32}{9 \cdot 3 ^{\frac{1}{4}}})

+1

Interval Notation

Domain : [- 2, 0] \cup [2, \infty)

Range : [0, \infty)

Solution steps

Domain of

\frac{1}{2} (x^{3} - 4 x)^{\frac{3}{2}} : - 2 \leq x \leq 0 or x \geq 2

Range of

\frac{1}{2} (x^{3} - 4 x)^{\frac{3}{2}} : f (x) \geq 0

Axis interception points of

\frac{1}{2} (x^{3} - 4 x)^{\frac{3}{2}} :

X Intercepts

: (0, 0), (- 2, 0), (2, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{1}{2} (x^{3} - 4 x)^{\frac{3}{2}} :

None

Extreme Points of

\frac{1}{2} (x^{3} - 4 x)^{\frac{3}{2}} :

Minimum

(- 2, 0),

Maximum

(- \frac{2}{3 ^{\frac{1}{2}}}, \frac{32}{9 \cdot 3 ^{\frac{1}{4}}})

Graph

Popular Examples

f(x)=ln(x^2-4x+5)

f(x)=(x^3-2)/(x^4)

f(x)= 3/(x+1)-2

Frequently Asked Questions (FAQ)

What is the y= 1/2 (x^3-4x)^{3/2} ?
The y= 1/2 (x^3-4x)^{3/2} is