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

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

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extreme 5x+5sin(x)

extreme

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))

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