What is the extreme f(x)=sin(x)-cos(x),0<= x<= pi ?

The extreme f(x)=sin(x)-cos(x),0<= x<= pi is Minimum(0,-1),Maximum((3pi)/4 ,sqrt(2)),Minimum(pi,1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=sin(x)-cos(x),0<= x<= pi

extreme points

f (x) = sin (x) - cos (x), 0 \leq x \leq π

Minimum (0, - 1), Maximum (\frac{3 π}{4}, 2), Minimum (π, 1)

Solution steps

Find the critical points:

x = 0, x = \frac{3 π}{4}, x = π

Domain of

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

Find intervals:

Increasing

: 0 < x < \frac{3 π}{4},

Decreasing

: \frac{3 π}{4} < x < π

Plug the extreme point

x = 0

into

sin (x) - cos (x) \Rightarrow y = - 1

Minimum (0, - 1)

Plug the extreme point

x = \frac{3 π}{4}

into

sin (x) - cos (x) \Rightarrow y = 2

Maximum (\frac{3 π}{4}, 2)

Plug the extreme point

x = π

into

sin (x) - cos (x) \Rightarrow y = 1

Minimum (π, 1)

Minimum (0, - 1), Maximum (\frac{3 π}{4}, 2), Minimum (π, 1)

f (x) = \frac{x}{e ^{x}}

f (x) = 3 (x - 5)^{2} + 1

f (x, y) = 2 x^{2} + y^{2} + 8 x - 6 y + 20

f (x, y) = 3 x + 4 x y + 2 y^{3} - 8

f (x) = \frac{4 x}{3 x ^{2} + 27}

What is the extreme f(x)=sin(x)-cos(x),0<= x<= pi ?
The extreme f(x)=sin(x)-cos(x),0<= x<= pi is Minimum(0,-1),Maximum((3pi)/4 ,sqrt(2)),Minimum(pi,1)