What is the extreme f(x)=6sin(2x) ?

The extreme f(x)=6sin(2x) is Maximum(pi/4+pin,6),Minimum((3pi)/4+pin,-6)

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extreme f(x)=6sin(2x)

extreme points

f (x) = 6 sin (2 x)

Maximum (\frac{π}{4} + πn, 6), Minimum (\frac{3 π}{4} + πn, - 6)

Solution steps

Find the critical points:

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

Domain of

6 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

6 sin (2 x) \Rightarrow y = 6

Maximum (\frac{π}{4} + πn, 6)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

6 sin (2 x) \Rightarrow y = - 6

Minimum (\frac{3 π}{4} + πn, - 6)

Maximum (\frac{π}{4} + πn, 6), Minimum (\frac{3 π}{4} + πn, - 6)

x^{2} + 2 x + 6

f (x) = x^{2} + 2 y^{2} - 4 x + 12 y

x^{2} - 6 x + 4

x^{2} - 6 x + 9

f (x) = - 2 x^{3} + 6 x^{2} - 7

What is the extreme f(x)=6sin(2x) ?
The extreme f(x)=6sin(2x) is Maximum(pi/4+pin,6),Minimum((3pi)/4+pin,-6)