What is the extreme x(sqrt(8-x^2)) ?

The extreme x(sqrt(8-x^2)) is Maximum(-2sqrt(2),0),Minimum(-2,-4),Maximum(2,4),Minimum(2sqrt(2),0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme x(sqrt(8-x^2))

extreme

Maximum (- 22, 0), Minimum (- 2, - 4), Maximum (2, 4), Minimum (22, 0)

Solution steps

Find the critical points:

x = - 22, x = - 2, x = 2, x = 22

Domain of

x 8 - x^{2} : - 22 \leq x \leq 22

Find intervals:

Decreasing

: - 22 < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < 22

Plug the extreme point

x = - 22

into

x 8 - x^{2} \Rightarrow y = 0

Maximum (- 22, 0)

Plug the extreme point

x = - 2

into

x 8 - x^{2} \Rightarrow y = - 4

Minimum (- 2, - 4)

Plug the extreme point

x = 2

into

x 8 - x^{2} \Rightarrow y = 4

Maximum (2, 4)

Plug the extreme point

x = 22

into

x 8 - x^{2} \Rightarrow y = 0

Minimum (22, 0)

Maximum (- 22, 0), Minimum (- 2, - 4), Maximum (2, 4), Minimum (22, 0)

What is the extreme x(sqrt(8-x^2)) ?
The extreme x(sqrt(8-x^2)) is Maximum(-2sqrt(2),0),Minimum(-2,-4),Maximum(2,4),Minimum(2sqrt(2),0)