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Popular >

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

Solution

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

Solution

Domain : - 1 \leq x \leq 1

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

X Intercepts : (0, 0), (1, 0), (- 1, 0), Y Intercepts : (0, 0)

Asymptotes : None

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

+1

Interval Notation

Domain : [- 1, 1]

Range : [- \frac{1}{2 ^{\frac{1}{2}} 2}, \frac{1}{2 ^{\frac{1}{2}} 2}]

Solution steps

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

: (0, 0), (1, 0), (- 1, 0),

Y Intercepts

: (0, 0)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(- 1, 0),

Minimum

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

Maximum

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

Minimum

(1, 0)

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

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Frequently Asked Questions (FAQ)

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