What is the extreme f(x)=5x+5sin(x),0<= x<= 2pi ?

The extreme f(x)=5x+5sin(x),0<= x<= 2pi is Minimum(0,0),Saddle(pi,5pi),Maximum(2pi,10pi)

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extreme f(x)=5x+5sin(x),0<= x<= 2pi

extreme points

f (x) = 5 x + 5 sin (x), 0 \leq x \leq 2 π

Minimum (0, 0), Saddle (π, 5 π), Maximum (2 π, 10 π)

Solution steps

Find the critical points:

x = 0, x = π, x = 2 π

Domain of

5 x + 5 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

5 x + 5 sin (x) \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = π

into

5 x + 5 sin (x) \Rightarrow y = 5 π

Saddle (π, 5 π)

Plug the extreme point

x = 2 π

into

5 x + 5 sin (x) \Rightarrow y = 10 π

Maximum (2 π, 10 π)

Minimum (0, 0), Saddle (π, 5 π), Maximum (2 π, 10 π)

f (x) = \frac{1}{2} x + 2, - 3 \leq x \leq 3

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

f (x) = 2 x^{2} + 4 x + 10

f (x) = 1 - x^{3} - 3 x - 2 x^{2} + 3 x^{4}

f (x) = (x - 1) (x + 2) (x + 4)

What is the extreme f(x)=5x+5sin(x),0<= x<= 2pi ?
The extreme f(x)=5x+5sin(x),0<= x<= 2pi is Minimum(0,0),Saddle(pi,5pi),Maximum(2pi,10pi)