VIbarguen1
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



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anonymous
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did you take the derivative?

VIbarguen1
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Yep I got f'(x) = 2 sin(x) cos (2x) + 5 /cos (2x)3 )^2

VIbarguen1
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it is so long im not sure its right

VIbarguen1
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@satellite73

VIbarguen1
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@RaphaelFilgueiras

RaphaelFilgueiras
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dw:1389408369353:dw

VIbarguen1
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could you help me solve that I have no idea how

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

RaphaelFilgueiras
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dw:1389408745656:dw

VIbarguen1
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raphael i'm sorry i am not following, where did the Z come from? and how does that get me to the extrema?

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

RaphaelFilgueiras
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x= 0 and 2 pi will be your solutions


VIbarguen1
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is that my min and max solutions?

VIbarguen1
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and it would be decreasing because its positive right?

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

VIbarguen1
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ok got it

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

RaphaelFilgueiras
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decreasing f'<0
increasing f'>0

VIbarguen1
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thank you so much

RaphaelFilgueiras
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you are welcome