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

The extreme f(x)=3+sin((2pi)/3 x) is Maximum(3/4+3n,4),Minimum(9/4+3n,2)

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extreme f(x)=3+sin((2pi)/3 x)

extreme points

f (x) = 3 + sin (\frac{2 π}{3} x)

Maximum (\frac{3}{4} + 3 n, 4), Minimum (\frac{9}{4} + 3 n, 2)

Solution steps

Find the critical points:

x = \frac{3}{4} + 3 n, x = \frac{9}{4} + 3 n

Domain of

3 + sin (\frac{2 π}{3} x) : - \infty < x < \infty

Find intervals:

Increasing

: 3 n \leq x < \frac{3}{4} + 3 n,

Decreasing

: \frac{3}{4} + 3 n < x < \frac{9}{4} + 3 n,

Increasing

: \frac{9}{4} + 3 n < x < 3 + 3 n

Plug the extreme point

x = \frac{3}{4} + 3 n

into

3 + sin (\frac{2 π}{3} x) \Rightarrow y = 4

Maximum (\frac{3}{4} + 3 n, 4)

Plug the extreme point

x = \frac{9}{4} + 3 n

into

3 + sin (\frac{2 π}{3} x) \Rightarrow y = 2

Minimum (\frac{9}{4} + 3 n, 2)

Maximum (\frac{3}{4} + 3 n, 4), Minimum (\frac{9}{4} + 3 n, 2)

e x t re m e f (x) = ln (2 - 5 x^{2})

d o main f (x) = \frac{1}{4 x - 3}

l c m 13, - 11

in v erse f (x) = ln (x - 2)

in v erse f (x) = \frac{3}{5} x

What is the extreme f(x)=3+sin((2pi)/3 x) ?
The extreme f(x)=3+sin((2pi)/3 x) is Maximum(3/4+3n,4),Minimum(9/4+3n,2)