Question

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.

Answer 1

Sometimes, you just gotta learn to listen to those whispers in your ear ^^

Answer 2

So, when you hear "slope of the tangent", something should always whisper "derivative" in your ear :D

What's the derivative of xcos(x) ?

Answer 3

x-sinx+cosx

Answer 4

Umm... somehow, I feel you have the right idea, but your answer is off ^^
There should only be two terms.

Answer 5

I bet you meant x(-sin(x)) + cos(x)

Answer 6

Yes! I did I'm sorry

Answer 7

Be more careful next time ^^
Your teacher will probably not be as considerate :D

Anyway, this comes down to
y' = cos(x) - xsin(x)

Answer 8

yes

Answer 9

Well, this derivative IS the slope of the tangent line.
So... when is this equal to zero?

0 = cos(x) - xsin(x)

Answer 10

I'm not sure to be honest

Answer 11

I'm not sure how to find that

Answer 12

You just have to be creative ^^
Here. It means
\[\large \cos(x) = x\sin(x)\]
Maybe you can work it out from here

Answer 13

oh shoot

Answer 14

x=cosx/sinx

Answer 15

and cosx/sinx=tanx

Answer 16

uhhh, no.
\[\large \frac{\sin(x)}{\cos(x)}=\tan(x)\]

Answer 17

wow sorry as you can tell I'm really bad at this

Answer 18

But this should put you on the right track ^^

Answer 19

Sure, you're right about \[\large x = \frac{\cos(x)}{\sin(x)}\]
This should bring you really close to the answer :D

Answer 20

would it be 1/x? becasue we want to change sinx/cosx into cosx/sinx

Answer 21

That's right ^^

Answer 22

I understand now, i just have to remember cosx/sinx is equal to tanx. thank you

Answer 23

As you can see

Answer 24

You're not as bad at this as you think :)

Answer 25

:) thank you