What is the extreme f(x)=-sin(x)-4 ?

The extreme f(x)=-sin(x)-4 is Minimum(pi/2+2pin,-5),Maximum((3pi)/2+2pin,-3)

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extreme f(x)=-sin(x)-4

extreme points

f (x) = - sin (x) - 4

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

Solution steps

Find the critical points:

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

Domain of

- sin (x) - 4 : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Increasing

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

Decreasing

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

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

- sin (x) - 4 \Rightarrow y = - 5

Minimum (\frac{π}{2} + 2 πn, - 5)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

- sin (x) - 4 \Rightarrow y = - 3

Maximum (\frac{3 π}{2} + 2 πn, - 3)

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

f (x) = 2 x^{3} - x^{2} - 4 x + 8 (- 1)

f (x, y) = 2 x^{5} + x^{3} y^{2} + 6 x y^{4}

f (x, y) = x^{2} - 2 x^{3} + 2 x^{2} + 3 x y

f (x, y) = x^{2} y^{3} - (x - 2 y)^{2} + 6 x^{4} y = 3 x y

f (x) = 2 x^{4} - 20 x^{2} + 18

What is the extreme f(x)=-sin(x)-4 ?
The extreme f(x)=-sin(x)-4 is Minimum(pi/2+2pin,-5),Maximum((3pi)/2+2pin,-3)