What is the extreme f(x)=4cos^2(x) ?

The extreme f(x)=4cos^2(x) is Maximum(pin,4),Minimum(pi/2+pin,0)

Popular >

extreme f(x)=4cos^2(x)

extreme points

f (x) = 4 cos^{2} (x)

Maximum (πn, 4), Minimum (\frac{π}{2} + πn, 0)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

4 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

4 cos^{2} (x) \Rightarrow y = 4

Maximum (πn, 4)

Plug the extreme point

x = \frac{π}{2} + πn

into

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

Minimum (\frac{π}{2} + πn, 0)

Maximum (πn, 4), Minimum (\frac{π}{2} + πn, 0)

f (x) = 2 x^{3} - 24 x + 1

g (x, y) = e^{x} - x + e^{y} - y

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

f (x) = (x + 8)^{\frac{2}{3}}

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

What is the extreme f(x)=4cos^2(x) ?
The extreme f(x)=4cos^2(x) is Maximum(pin,4),Minimum(pi/2+pin,0)