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

The extreme f(x)=5cos(x),0<= x<= 2pi is Maximum(0,5),Minimum(pi,-5),Maximum(2pi,5)

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

extreme points

f (x) = 5 cos (x), 0 \leq x \leq 2 π

Maximum (0, 5), Minimum (π, - 5), Maximum (2 π, 5)

Solution steps

Find the critical points:

x = 0, x = π, x = 2 π

Domain of

5 cos (x), 0 \leq x \leq 2 π : 0 \leq x \leq 2 π

Find intervals:

Decreasing

: 0 < x < π,

Increasing

: π < x < 2 π

Plug the extreme point

x = 0

into

5 cos (x) \Rightarrow y = 5

Maximum (0, 5)

Plug the extreme point

x = π

into

5 cos (x) \Rightarrow y = - 5

Minimum (π, - 5)

Plug the extreme point

x = 2 π

into

5 cos (x) \Rightarrow y = 5

Maximum (2 π, 5)

Maximum (0, 5), Minimum (π, - 5), Maximum (2 π, 5)

f (x) = \frac{1}{( x + 2 )}

f (x) = x - 6

y = 8 x - ln (8 x)

f (x) = \frac{x ^{2} + 3}{x ^{2} + 1}

y = \frac{4}{5} x + \frac{9}{4}

What is the extreme f(x)=5cos(x),0<= x<= 2pi ?
The extreme f(x)=5cos(x),0<= x<= 2pi is Maximum(0,5),Minimum(pi,-5),Maximum(2pi,5)