anonymous
  • anonymous
For x not equal to 0, the slope of the tangent to y=xcosx equals zero whenever 1.) tanx=-x 2.)tanx=(1/x) 3.)tanx=x 4.)sinx=x 5.)cosx=x Please help, explanation would be greatly appreciated.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Sometimes, you just gotta learn to listen to those whispers in your ear ^^
anonymous
  • anonymous
So, when you hear "slope of the tangent", something should always whisper "derivative" in your ear :D What's the derivative of xcos(x) ?
anonymous
  • anonymous
x-sinx+cosx

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anonymous
  • anonymous
Umm... somehow, I feel you have the right idea, but your answer is off ^^ There should only be two terms.
anonymous
  • anonymous
I bet you meant x(-sin(x)) + cos(x)
anonymous
  • anonymous
Yes! I did I'm sorry
anonymous
  • anonymous
Be more careful next time ^^ Your teacher will probably not be as considerate :D Anyway, this comes down to y' = cos(x) - xsin(x)
anonymous
  • anonymous
yes
anonymous
  • anonymous
Well, this derivative IS the slope of the tangent line. So... when is this equal to zero? 0 = cos(x) - xsin(x)
anonymous
  • anonymous
I'm not sure to be honest
anonymous
  • anonymous
I'm not sure how to find that
anonymous
  • anonymous
You just have to be creative ^^ Here. It means \[\large \cos(x) = x\sin(x)\] Maybe you can work it out from here
anonymous
  • anonymous
oh shoot
anonymous
  • anonymous
x=cosx/sinx
anonymous
  • anonymous
and cosx/sinx=tanx
anonymous
  • anonymous
uhhh, no. \[\large \frac{\sin(x)}{\cos(x)}=\tan(x)\]
anonymous
  • anonymous
wow sorry as you can tell I'm really bad at this
anonymous
  • anonymous
But this should put you on the right track ^^
anonymous
  • anonymous
Sure, you're right about \[\large x = \frac{\cos(x)}{\sin(x)}\] This should bring you really close to the answer :D
anonymous
  • anonymous
would it be 1/x? becasue we want to change sinx/cosx into cosx/sinx
anonymous
  • anonymous
That's right ^^
anonymous
  • anonymous
I understand now, i just have to remember cosx/sinx is equal to tanx. thank you
anonymous
  • anonymous
As you can see
anonymous
  • anonymous
You're not as bad at this as you think :)
anonymous
  • anonymous
:) thank you

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