What is the extreme f(x)=5cos^2(x) ?

The extreme f(x)=5cos^2(x) is Maximum(pin,5),Minimum(pi/2+pin,0)

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extreme f(x)=5cos^2(x)

extreme points

f (x) = 5 cos^{2} (x)

Maximum (πn, 5), Minimum (\frac{π}{2} + πn, 0)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

5 cos^{2} (x) : - \infty < x < \infty

Find intervals:

Decreasing

: πn < x < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

5 cos^{2} (x) \Rightarrow y = 5

Maximum (πn, 5)

Plug the extreme point

x = \frac{π}{2} + πn

into

5 cos^{2} (x) \Rightarrow y = 0

Minimum (\frac{π}{2} + πn, 0)

Maximum (πn, 5), Minimum (\frac{π}{2} + πn, 0)

f (x) = x - e^{x}

f (x) = x^{3} + 1

m = - \frac{2}{3}, (0, - 2)

f (x) = 8 x + 2

What is the extreme f(x)=5cos^2(x) ?
The extreme f(x)=5cos^2(x) is Maximum(pin,5),Minimum(pi/2+pin,0)