What is the extreme f(x)=-3sin(2x)-4 ?

The extreme f(x)=-3sin(2x)-4 is Minimum(pi/4+pin,-7),Maximum((3pi)/4+pin,-1)

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extreme f(x)=-3sin(2x)-4

extreme points

f (x) = - 3 sin (2 x) - 4

Minimum (\frac{π}{4} + πn, - 7), Maximum (\frac{3 π}{4} + πn, - 1)

Solution steps

Find the critical points:

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

Domain of

- 3 sin (2 x) - 4 : - \infty < x < \infty

Find intervals:

Decreasing

: πn \leq x < \frac{π}{4} + πn,

Increasing

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

Decreasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

- 3 sin (2 x) - 4 \Rightarrow y = - 7

Minimum (\frac{π}{4} + πn, - 7)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

- 3 sin (2 x) - 4 \Rightarrow y = - 1

Maximum (\frac{3 π}{4} + πn, - 1)

Minimum (\frac{π}{4} + πn, - 7), Maximum (\frac{3 π}{4} + πn, - 1)

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

f (x) = 2 sin^{2} (x), 0 \leq x \leq π

f (x) = 4 cos (3 x) + 5, (0, 2 π)

f (x, y) = 14 x y - x^{3} - 7 y^{2}

f (x, y) = x^{2} + x y + y^{2} - 25 y + 208

What is the extreme f(x)=-3sin(2x)-4 ?
The extreme f(x)=-3sin(2x)-4 is Minimum(pi/4+pin,-7),Maximum((3pi)/4+pin,-1)