What is the extreme y=3sin(x)+sqrt(3)cos(x) ?

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

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extreme y=3sin(x)+sqrt(3)cos(x)

extreme

Maximum (\frac{π}{3} + 2 πn, 23), Minimum (\frac{4 π}{3} + 2 πn, - 23)

Solution steps

Find the critical points:

x = \frac{π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Domain of

3 sin (x) + 3 cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{3} + 2 πn,

Decreasing

: \frac{π}{3} + 2 πn < x < \frac{4 π}{3} + 2 πn,

Increasing

: \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{3} + 2 πn

into

3 sin (x) + 3 cos (x) \Rightarrow y = 23

Maximum (\frac{π}{3} + 2 πn, 23)

Plug the extreme point

x = \frac{4 π}{3} + 2 πn

into

3 sin (x) + 3 cos (x) \Rightarrow y = - 23

Minimum (\frac{4 π}{3} + 2 πn, - 23)

Maximum (\frac{π}{3} + 2 πn, 23), Minimum (\frac{4 π}{3} + 2 πn, - 23)

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