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Popular >

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

Solution

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

Solution

Domain : - 2 \leq x \leq 2

Range : - 2 \cdot 2^{\frac{1}{2}} \leq f (x) \leq 2 \cdot 2^{\frac{1}{2}}

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

Asymptotes : None

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

+1

Solution steps

Domain of

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

Range of

x (4 - x^{2})^{\frac{1}{2}} : - 2 \cdot 2^{\frac{1}{2}} \leq f (x) \leq 2 \cdot 2^{\frac{1}{2}}

Axis interception points of

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

X Intercepts

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

Y Intercepts

: (0, 0)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(- 2, 0),

Minimum

(- 2, - 2 \cdot 2^{\frac{1}{2}}),

Maximum

(2, 2 \cdot 2^{\frac{1}{2}}),

Minimum

(2, 0)

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Frequently Asked Questions (FAQ)

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