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

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

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extreme f(x)=6sin(x)

extreme points

f (x) = 6 sin (x)

Maximum (\frac{π}{2} + 2 πn, 6), Minimum (\frac{3 π}{2} + 2 πn, - 6)

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Decreasing

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

Increasing

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

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

6 sin (x) \Rightarrow y = 6

Maximum (\frac{π}{2} + 2 πn, 6)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

6 sin (x) \Rightarrow y = - 6

Minimum (\frac{3 π}{2} + 2 πn, - 6)

Maximum (\frac{π}{2} + 2 πn, 6), Minimum (\frac{3 π}{2} + 2 πn, - 6)

f (x) = x + 1 + 1 - x

f (x) = x^{3} - 3 x^{2} + 5 x - 6

x^{2} + x - 2

f (x) = x e^{- 2 x^{2}}

f (x, y) = \frac{1}{x} + x y + \frac{1}{y}

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