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

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

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

extreme points

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

Saddle (\frac{π}{3} + \frac{2 πn}{3}, π + 2 πn + sin (π + 2 πn))

Solution steps

Find the critical points:

x = \frac{π}{3} + \frac{2 πn}{3}

Domain of

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

Find intervals:

Increasing

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

Increasing

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

Plug the extreme point

x = \frac{π}{3} + \frac{2 πn}{3}

into

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

Saddle (\frac{π}{3} + \frac{2 πn}{3}, π + 2 πn + sin (π + 2 πn))

f (x) = 6 x^{3} - 9 x^{2} - 216 x + 7, - 4 \leq x \leq 5

e^{x^{2} + 3 \cdot x + 4}

f (x) = x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12

f (x) = x^{3} - 4 x^{2} - 3 x^{2} + 6

f (x, y) = (x^{2} + y^{2}) (e^{x + y})

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