What is the extreme y=x-sin(-x),0<= x<= 2pi ?

The extreme y=x-sin(-x),0<= x<= 2pi is Minimum(0,0),Saddle(pi,pi),Maximum(2pi,2pi)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme y=x-sin(-x),0<= x<= 2pi

extreme points

y = x - sin (- x), 0 \leq x \leq 2 π

Minimum (0, 0), Saddle (π, π), Maximum (2 π, 2 π)

Solution steps

Find the critical points:

x = 0, x = π, x = 2 π

Domain of

x - sin (- x), 0 \leq x \leq 2 π : 0 \leq x \leq 2 π

Find intervals:

Increasing

: 0 < x < π,

Increasing

: π < x < 2 π

Plug the extreme point

x = 0

into

x - sin (- x) \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = π

into

x - sin (- x) \Rightarrow y = π

Saddle (π, π)

Plug the extreme point

x = 2 π

into

x - sin (- x) \Rightarrow y = 2 π

Maximum (2 π, 2 π)

Minimum (0, 0), Saddle (π, π), Maximum (2 π, 2 π)

x^{2} (2 - x)^{3}

f (x, y) = 2 x^{2} - 5 y^{2} + 6 y

f (x, y) = (x + y)

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

cos (4 x)

What is the extreme y=x-sin(-x),0<= x<= 2pi ?
The extreme y=x-sin(-x),0<= x<= 2pi is Minimum(0,0),Saddle(pi,pi),Maximum(2pi,2pi)