What is the extreme f(x)=5x+5sin(x) ?

The extreme f(x)=5x+5sin(x) is Saddle(pi+2pin,5(pi+2pin)+5sin(pi+2pin))

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extreme f(x)=5x+5sin(x)

extreme points

f (x) = 5 x + 5 sin (x)

Saddle (π + 2 πn, 5 (π + 2 πn) + 5 sin (π + 2 πn))

Solution steps

Find the critical points:

x = π + 2 πn

Domain of

5 x + 5 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

5 x + 5 sin (x) \Rightarrow y = 5 (π + 2 πn) + 5 sin (π + 2 πn)

Saddle (π + 2 πn, 5 (π + 2 πn) + 5 sin (π + 2 πn))

f (x) = 5 - 3 sin (2 x)

\frac{2 x - 4}{3}

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

f (x) = x^{3} - 3 x, 0 \leq x \leq 2

2 x - x

What is the extreme f(x)=5x+5sin(x) ?
The extreme f(x)=5x+5sin(x) is Saddle(pi+2pin,5(pi+2pin)+5sin(pi+2pin))