anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
did you take the derivative?
anonymous
  • anonymous
Yep I got f'(x) = 2 sin(x) cos (2x) + 5 /cos (2x)-3 )^2
anonymous
  • anonymous
it is so long im not sure its right

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anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
@RaphaelFilgueiras
anonymous
  • anonymous
|dw:1389408369353:dw|
anonymous
  • anonymous
could you help me solve that I have no idea how
anonymous
  • anonymous
use sin²(x)+cos²(x)=1-> cos²(x)=1-sin²(x), and then you will have only sin x in your equations
anonymous
  • anonymous
|dw:1389408745656:dw|
anonymous
  • anonymous
raphael i'm sorry i am not following, where did the Z come from? and how does that get me to the extrema?
anonymous
  • anonymous
Z means k belong to the interger set,it's just a generical ans
anonymous
  • anonymous
x= 0 and 2 pi will be your solutions
anonymous
  • anonymous
and pi
anonymous
  • anonymous
is that my min and max solutions?
anonymous
  • anonymous
and it would be decreasing because its positive right?
anonymous
  • anonymous
min x= pi max are both x=0 and 2pi
anonymous
  • anonymous
ok got it
anonymous
  • anonymous
when sin(x)> 0 it will be decreasing x in]0,pi[ when sinx(x)<0 it will be increasing x in ]pi,2pi[
anonymous
  • anonymous
decreasing f'<0 increasing f'>0
anonymous
  • anonymous
thank you so much
anonymous
  • anonymous
you are welcome

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