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

The extreme f(x)=(sin(x)+cos(x))^2 is Maximum(pi/4+pin,2),Minimum((3pi)/4+pin,0)

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extreme f(x)=(sin(x)+cos(x))^2

extreme points

f (x) = (sin (x) + cos (x))^{2}

Maximum (\frac{π}{4} + πn, 2), Minimum (\frac{3 π}{4} + πn, 0)

Solution steps

Find the critical points:

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Domain of

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

Find intervals:

Increasing

: πn \leq x < \frac{π}{4} + πn,

Decreasing

: \frac{π}{4} + πn < x < \frac{3 π}{4} + πn,

Increasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

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

Maximum (\frac{π}{4} + πn, 2)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

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

Minimum (\frac{3 π}{4} + πn, 0)

Maximum (\frac{π}{4} + πn, 2), Minimum (\frac{3 π}{4} + πn, 0)

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + 8

f (x) = - 4 (x - 1)^{\frac{4}{7}} + 8

f (x) = 2 x^{2} - 4 x + 6

f (x) = 2 x (196 - x^{2})

f (x, y) = 13 - 4 x - 5 y

What is the extreme f(x)=(sin(x)+cos(x))^2 ?
The extreme f(x)=(sin(x)+cos(x))^2 is Maximum(pi/4+pin,2),Minimum((3pi)/4+pin,0)