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

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

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extreme f(x)=4sin(x)+2

extreme points

f (x) = 4 sin (x) + 2

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

Solution steps

Find the critical points:

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

Domain of

4 sin (x) + 2 : - \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

4 sin (x) + 2 \Rightarrow y = 6

Maximum (\frac{π}{2} + 2 πn, 6)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

4 sin (x) + 2 \Rightarrow y = - 2

Minimum (\frac{3 π}{2} + 2 πn, - 2)

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

f (x) = 9 x ln (x)

f (x) = 8 x + 9 x^{\frac{8}{9}}

f (x, y) = 3 x^{2} - 2 x y + y^{2} - 8 y

f (x) = - 5 x + 3 ln (4 x)

f (x, y) = x y + 4 x

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