Question

find the intervals for which f is increasing or decreasing and locate all relative extrema on (0,2pi).

f(x)= cos x / 1 + sin x

Answer 1

@satellite73

Answer 2

First thing to do: differentiate it.

Answer 3

I got -1/(sinx + 1)

Answer 4

Now, if the graph is increasing, the slope increases.
If the graph decreases, the slope decreses.
For any extrema, the slope is zero.

Answer 5

Solve the following 3 equations to get each answers.
\[\frac{ -1 }{ \sin x + 1 }=0\]
\[\frac{ -1 }{ \sin x + 1 } > 0\]
\[\frac{ -1 }{ \sin x + 1 }<0\]
where x is in the interval (0,2pi)

Answer 6

First equation for relative extrema
Second equation for the interval the the graph increases
Third equation for the interval that the graph decreases

Answer 7

THANK YOU

Answer 8

Welcome :)

Answer 9

@science0229

Answer 10

I got another problem almost the same but instead its
f(x)= cos x / 1 + sin ^ 2x

Answer 11

could you help me?

Answer 12

I will post a new question :)

Answer 13

Same process, with longer time.
Differentiate it, first.