What is the extreme f(x)=cos^{(2)}(x)-sqrt(2)sin(x) ?

The extreme f(x)=cos^{(2)}(x)-sqrt(2)sin(x) is

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extreme f(x)=cos^{(2)}(x)-sqrt(2)sin(x)

extreme points

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

Minimum (\frac{π}{2} + 2 πn, - 2), Maximum (\frac{5 π}{4} + 2 πn, \frac{3}{2}), Minimum (\frac{3 π}{2} + 2 πn, 2), Maximum (\frac{7 π}{4} + 2 πn, \frac{3}{2})

Solution steps

Find the critical points:

x = \frac{π}{2} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{7 π}{4} + 2 πn

Domain of

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

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 2 πn < x < \frac{5 π}{4} + 2 πn,

Decreasing

: \frac{5 π}{4} + 2 πn < x < \frac{3 π}{2} + 2 πn,

Increasing

: \frac{3 π}{2} + 2 πn < x < \frac{7 π}{4} + 2 πn,

Decreasing

: \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

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

Minimum (\frac{π}{2} + 2 πn, - 2)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

cos^{2} (x) - 2 sin (x) \Rightarrow y = \frac{3}{2}

Maximum (\frac{5 π}{4} + 2 πn, \frac{3}{2})

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

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

Minimum (\frac{3 π}{2} + 2 πn, 2)

Plug the extreme point

x = \frac{7 π}{4} + 2 πn

into

cos^{2} (x) - 2 sin (x) \Rightarrow y = \frac{3}{2}

Maximum (\frac{7 π}{4} + 2 πn, \frac{3}{2})

Minimum (\frac{π}{2} + 2 πn, - 2), Maximum (\frac{5 π}{4} + 2 πn, \frac{3}{2}), Minimum (\frac{3 π}{2} + 2 πn, 2), Maximum (\frac{7 π}{4} + 2 πn, \frac{3}{2})

x^{3} + y^{4} - 9 x - 16 y^{2}

f (x, y) = e^{x y - 2} + (x - 1) y

y = x - 1 - z + 1

f (x) = x^{3} - 3 x^{2} - 9 x + 1, (0, 5)

f (x) x^{3} - 6 x^{2} + 9 x + 1

What is the extreme f(x)=cos^{(2)}(x)-sqrt(2)sin(x) ?
The extreme f(x)=cos^{(2)}(x)-sqrt(2)sin(x) is