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

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

Popular >

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

extreme points

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) = 106 x - x^{2} - 950

f (x) = \frac{- 3 x}{x ^{2} + 6}

f (x) = \frac{1}{x ^{2} - 4 x - 21}

P (x, y) = 16 x^{2} - 9 y^{2}

f (x) = 1920 x - 10 x^{3}

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