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

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

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extreme y=5cos^2(x)

extreme points

y = 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)

h (x, t) = 1.5 + lo g_{3} (x) (t + 1)

\frac{3200}{x} + 200 + 50 x

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

f (x, y) = - 2 x^{2} + 16 x - y^{2} + 6 y - 30

f (x) = 2 x - \frac{1}{2} (\frac{x}{50})^{2} - 1000

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