## VIbarguen1 one year ago Cal help? find the intervals for which f is increasing or decreasing and locate all relative extrema on (0,2pi). f(x)= cos x / 1 + sin ^ 2x

1. satellite73

did you take the derivative?

2. VIbarguen1

Yep I got f'(x) = 2 sin(x) cos (2x) + 5 /cos (2x)-3 )^2

3. VIbarguen1

it is so long im not sure its right

4. VIbarguen1

@satellite73

5. VIbarguen1

@RaphaelFilgueiras

6. RaphaelFilgueiras

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7. VIbarguen1

could you help me solve that I have no idea how

8. RaphaelFilgueiras

use sin²(x)+cos²(x)=1-> cos²(x)=1-sin²(x), and then you will have only sin x in your equations

9. RaphaelFilgueiras

|dw:1389408745656:dw|

10. VIbarguen1

raphael i'm sorry i am not following, where did the Z come from? and how does that get me to the extrema?

11. RaphaelFilgueiras

Z means k belong to the interger set,it's just a generical ans

12. RaphaelFilgueiras

x= 0 and 2 pi will be your solutions

13. RaphaelFilgueiras

and pi

14. VIbarguen1

is that my min and max solutions?

15. VIbarguen1

and it would be decreasing because its positive right?

16. RaphaelFilgueiras

min x= pi max are both x=0 and 2pi

17. VIbarguen1

ok got it

18. RaphaelFilgueiras

when sin(x)> 0 it will be decreasing x in]0,pi[ when sinx(x)<0 it will be increasing x in ]pi,2pi[

19. RaphaelFilgueiras

decreasing f'<0 increasing f'>0

20. VIbarguen1

thank you so much

21. RaphaelFilgueiras

you are welcome