please help me solve this much appreciated

Watch
maruchan
Badges: 12
Rep:
?
#1
Report Thread starter 1 year ago
#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
0
reply
the bear
Badges: 20
Rep:
?
#2
Report 1 year ago
#2
so are you trying to find stationary points ?

:holmes:
0
reply
maruchan
Badges: 12
Rep:
?
#3
Report Thread starter 1 year ago
#3
(Original post by the bear)
so are you trying to find stationary points ?

:holmes:
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 😄
0
reply
RDKGames
Badges: 20
Rep:
?
#4
Report 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 \cos 3x looks like, then slapping x in front of it is the same as making those waves come out tiny from the origin and grow infinitely big.
0
reply
the bear
Badges: 20
Rep:
?
#5
Report 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
1
reply
maruchan
Badges: 12
Rep:
?
#6
Report Thread starter 1 year ago
#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 \cos 3x looks like, then slapping x 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
0
reply
maruchan
Badges: 12
Rep:
?
#7
Report Thread starter 1 year ago
#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
reply
RDKGames
Badges: 20
Rep:
?
#8
Report 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 e^x - x = 0.
1
reply
maruchan
Badges: 12
Rep:
?
#9
Report Thread starter 1 year ago
#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 e^x - x = 0.
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
0
reply
RDKGames
Badges: 20
Rep:
?
#10
Report 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 \cot (3x) = 3x. You would not be expected to solve the impossible!
Last edited by RDKGames; 1 year ago
0
reply
maruchan
Badges: 12
Rep:
?
#11
Report Thread starter 1 year ago
#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 \cot x = 3x. 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
0
reply
RDKGames
Badges: 20
Rep:
?
#12
Report 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 \cot (3x) = 3x you just need to look at \cos 3x - 3x\sin 3x = 0 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.
0
reply
maruchan
Badges: 12
Rep:
?
#13
Report Thread starter 1 year ago
#13
(Original post by RDKGames)
For \cot (3x) = 3x you just need to look at \cos 3x - 3x\sin 3x = 0 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
0
reply
RDKGames
Badges: 20
Rep:
?
#14
Report 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.
0
reply
maruchan
Badges: 12
Rep:
?
#15
Report Thread starter 1 year ago
#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😂
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (77)
13.95%
I'm not sure (24)
4.35%
No, I'm going to stick it out for now (177)
32.07%
I have already dropped out (11)
1.99%
I'm not a current university student (263)
47.64%

Watched Threads

View All