intervalles monotones f(x)=cos(2x+5)

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monotone intervals f(x)=cos(2x+5)

Solution

Increasing:πn≤ x<−5+2π2 +πn, Decreasing:−5+2π2 +πn<x<3π−52 +πn, Increasing:3π−52 +πn<x<π+πn

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Monotone intervals definition

If f ′(x)>0 then f(x) is increasing.
If f ′(x)<0 then f(x) is decreasing.

Find the critical points: x=−5+2π2 +πn, x=3π−52 +πn

Domain of cos(2x+5) : −∞ <x<∞

Find intervals: Increasing:πn≤ x<−5+2π2 +πn, Decreasing:−5+2π2 +πn<x<3π−52 +πn, Increasing:3π−52 +πn<x<π+πn

Increasing:πn≤ x<−5+2π2 +πn, Decreasing:−5+2π2 +πn<x<3π−52 +πn, Increasing:3π−52 +πn<x<π+πn

Solve instead

domain cos(2x+5)

range cos(2x+5)

periodicity cos(2x+5)

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−▭▭	<	7	8	9	÷	`AC`
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×▭▭	(	1	2	3	−	`x`
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intervalles monotones f(x)=cos(2x+5)

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