anonymous
  • anonymous
Find all points on the graph of the function f(x) = 2 sin x + sin^2 x at which the tangent line is horizontal.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
f'(x) = sin2x i know that much
experimentX
  • experimentX
quite not ..
anonymous
  • anonymous
try finding the deivative again...(for asker)

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anonymous
  • anonymous
oh oh oh wait you're right hold up
anonymous
  • anonymous
i think it's better if you don't simplify f'(x)
anonymous
  • anonymous
nah i just didn't apply the product rule for the first term so i just had that as 0 but now i have f'(x) = 2 cos x sin 2 x
anonymous
  • anonymous
I MEAN 2 cos x + sin 2 x
anonymous
  • anonymous
ok, that's it... set = 0 to find your horizontal tangents...
anonymous
  • anonymous
uh rusty on trig run me through it
anonymous
  • anonymous
ok. your derivative is set to zero: 2cosx + sin2x = 0
anonymous
  • anonymous
|dw:1333128565642:dw| this is just the same but the derivative is not simplified... you can factor the left side of the equal sign...
anonymous
  • anonymous
like this: |dw:1333128666089:dw|
anonymous
  • anonymous
is it obvious what to do now?
anonymous
  • anonymous
set each factor to zero: |dw:1333128920266:dw|
anonymous
  • anonymous
for the first equation, where is cosine zero? what value?
anonymous
  • anonymous
still there?
anonymous
  • anonymous
yeah yeah wait
anonymous
  • anonymous
cos x = 0 @ x = pi/2, 3(pi)/2; sin x = 0 @ x = 0, pi
anonymous
  • anonymous
soooo
anonymous
  • anonymous
now what
anonymous
  • anonymous
sorry.. got sidetracked a bit... for the other factor: 1 + sinx = 0 sinx = -1 so x=3pi/2

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