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

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

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

extreme points

f (x) = 3 sin (2 x)

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

Solution steps

Find the critical points:

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

Domain of

3 sin (2 x) : - \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

3 sin (2 x) \Rightarrow y = 3

Maximum (\frac{π}{4} + πn, 3)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

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

Minimum (\frac{3 π}{4} + πn, - 3)

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

f (x, y) = 11 x^{2} + 4 x y + 5 y^{2} + 5 x + 5 y

f (x) = ln (\frac{1}{x ^{2} + 2 x + 10})

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

f (x, y) = 72 x + 30 y - 2 x^{2} - 3 y^{2}

y = \frac{( x ^{2} + 1 )}{( x ^{2} - 4 )}

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