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

The extreme f(x)=3x+3sin(x) is Saddle(pi+2pin,3(pi+2pin)+3sin(pi+2pin))

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extreme f(x)=3x+3sin(x)

extreme points

f (x) = 3 x + 3 sin (x)

Saddle (π + 2 πn, 3 (π + 2 πn) + 3 sin (π + 2 πn))

Solution steps

Find the critical points:

x = π + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = π + 2 πn

into

3 x + 3 sin (x) \Rightarrow y = 3 (π + 2 πn) + 3 sin (π + 2 πn)

Saddle (π + 2 πn, 3 (π + 2 πn) + 3 sin (π + 2 πn))

\frac{6}{x ^{2} + 3}

f (x) = 0.25 x^{2} + x + 2, (x \geq 0)

f (x) = \frac{x ^{3}}{3} - x

f (x) = x^{4} - 50 x^{2} + 1, - 4 \leq x \leq 11

f (x) = \frac{16}{x ^{2} + 4}

What is the extreme f(x)=3x+3sin(x) ?
The extreme f(x)=3x+3sin(x) is Saddle(pi+2pin,3(pi+2pin)+3sin(pi+2pin))