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)

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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)

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)