What is the extreme y=4x+4sin(x) ?

The extreme y=4x+4sin(x) is Saddle(pi+2pin,4(pi+2pin)+4sin(pi+2pin))

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extreme y=4x+4sin(x)

extreme points

y = 4 x + 4 sin (x)

Saddle (π + 2 πn, 4 (π + 2 πn) + 4 sin (π + 2 πn))

Solution steps

Find the critical points:

x = π + 2 πn

Domain of

4 x + 4 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

4 x + 4 sin (x) \Rightarrow y = 4 (π + 2 πn) + 4 sin (π + 2 πn)

Saddle (π + 2 πn, 4 (π + 2 πn) + 4 sin (π + 2 πn))

f (x, y) = x^{3} + y^{3} - 147 x - 75 y - 10

f (x) = x^{3} - 4 x^{2} - 16 x + 2

f (x) = x^{3} - 4 x^{2} - 16 x - 1

f (x, y) = 400 - 49 x^{2} - 64 y^{2}

f (x) = 2 x ln ∣ x ∣

What is the extreme y=4x+4sin(x) ?
The extreme y=4x+4sin(x) is Saddle(pi+2pin,4(pi+2pin)+4sin(pi+2pin))