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#1
hi guys could anyone help me solve the differential of xcos3x

I differentiated it to get
cos3x-3xsin3x=0

but I don't know what to do next. any help would be much appreciated.
thank you
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1 year ago
#2
so are you trying to find stationary points ?

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#3
(Original post by the bear)
so are you trying to find stationary points ?

yes, I am. so I can plot the graph and I need to solve it to get the turning points. do you know where I should go from here 😄
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1 year ago
#4
(Original post by maruchan)
yes, I am. so I can plot the graph and I need to solve it to get the turning points. do you know where I should go from here 😄
That's gonna be a lot of turning points... and obviously the derivative being zero constitutes a transcendental equation; you cant solve it for x.

I suggest you you first realise how looks like, then slapping in front of it is the same as making those waves come out tiny from the origin and grow infinitely big.
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1 year ago
#5
you can figure out the graph without actually finding the turning points ?

draw y = x and y = -x

now draw cos3x, but stretch it up and down so the max and mins touch the lines y = x and y = -x
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#6
(Original post by RDKGames)
That's gonna be a lot of turning points... and obviously the derivative being zero constitutes a transcendental equation; you cant solve it for x.

I suggest you you first realise how looks like, then slapping in front of it is the same as making those waves come out tiny from the origin and grow infinitely big.
ah right so there is no way I can solve that equation?

I was interested to see whether I could or not. as trying to figure it out sounds like a good idea too. thank you
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#7
(Original post by the bear)
you can figure out the graph without actually finding the turning points ?

draw y = x and y = -x

now draw cos3x, but stretch it up and down so the max and mins touch the lines y = x and y = -x
that's a great way thank you v much!
is there a way I can solve it though as I was intrigued to see whether I could or not. I tried using the double angle formula but it got complicated.. haha
1
1 year ago
#8
(Original post by maruchan)
ah right so there is no way I can solve that equation?
Nope.

Transcendental equations can't be solved by your usual analytical tricks, best you can do is approximate the solution via numerical methods -- clearly a bad idea for this question anyway.

Another example of a transcendental equation is the simple .
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#9
(Original post by RDKGames)
Nope.

Transcendental equations can't be solved by your usual analytical tricks, best you can do is approximate the solution via numerical methods -- clearly a bad idea for this question anyway.

Another example of a transcendental equation is the simple .
thank you for your help. I really appreciate it. I assumed it could be solved as it was given to me in a differentiation exercise so I assumed it must be linked? but now I know haha
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1 year ago
#10
(Original post by maruchan)
thank you for your help. I really appreciate it. I assumed it could be solved as it was given to me in a differentiation exercise so I assumed it must be linked? but now I know haha
Well it's probably testing just that; your differentiation skills.

The furthest this type of question would go is asking you to show that stationary points are solutions of . You would not be expected to solve the impossible!
Last edited by RDKGames; 1 year ago
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#11
(Original post by RDKGames)
Well it's probably testing just that; your differentiation skills.

The furthest this type of question would go is asking you to show that stationary points are solutions of . You would not be expected to solve the impossible!
so when you mean to show the stationary points how would I get to that bit😂 sorry for all the questions I think I overcomplicated everything
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1 year ago
#12
(Original post by maruchan)
so when you mean to show the stationary points how would I get to that bit😂 sorry for all the questions I think I overcomplicated everything
For you just need to look at and see if you can manipulate it a bit into the required form. Nothing complicated here, and I doubt this type of question ever even comes up.
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#13
(Original post by RDKGames)
For you just need to look at and see if you can manipulate it a bit into the required form. Nothing complicated here, and I doubt this type of question ever even comes up.
ah right thank you very much doubt I could solve that though even if I take the inverse cot or use a double angle formula
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1 year ago
#14
(Original post by maruchan)
ah right thank you very much doubt I could solve that though even if I take the inverse cot or use a double angle formula
Yes but ive been saying this for the last few posts now... you cant solve that! And the question I proposed isnt even asking you to, its just asking you to obtain that form thats all.
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#15
(Original post by RDKGames)
Yes but ive been saying this for the last few posts now... you cant solve that! And the question I proposed isnt even asking you to, its just asking you to obtain that form thats all.
I know sorry for asking multiple times can I solve it . I always do that with questions hoping that maybe it can be solved😂
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