What is the extreme f(x)=xsqrt(4-x^2) ?

The extreme f(x)=xsqrt(4-x^2) is Maximum(-2,0),Minimum(-sqrt(2),-2),Maximum(sqrt(2),2),Minimum(2,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=xsqrt(4-x^2)

extreme points

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

Maximum (- 2, 0), Minimum (- 2, - 2), Maximum (2, 2), Minimum (2, 0)

Solution steps

Find the critical points:

x = - 2, x = - 2, x = 2, x = 2

Domain of

x 4 - x^{2} : - 2 \leq x \leq 2

Find intervals:

Decreasing

: - 2 < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < 2

Plug the extreme point

x = - 2

into

x 4 - x^{2} \Rightarrow y = 0

Maximum (- 2, 0)

Plug the extreme point

x = - 2

into

x 4 - x^{2} \Rightarrow y = - 2

Minimum (- 2, - 2)

Plug the extreme point

x = 2

into

x 4 - x^{2} \Rightarrow y = 2

Maximum (2, 2)

Plug the extreme point

x = 2

into

x 4 - x^{2} \Rightarrow y = 0

Minimum (2, 0)

Maximum (- 2, 0), Minimum (- 2, - 2), Maximum (2, 2), Minimum (2, 0)

y = - x^{6}

lo g_{10} (x^{2})

x^{4} - 8 x^{3}

f (x) = x^{4} + 6

\frac{2}{( \frac{2}{x} )}

What is the extreme f(x)=xsqrt(4-x^2) ?
The extreme f(x)=xsqrt(4-x^2) is Maximum(-2,0),Minimum(-sqrt(2),-2),Maximum(sqrt(2),2),Minimum(2,0)