please help me solve this much appreciated

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 😄

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.

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

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 $e^x - x = 0$.

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 $\cot x = 3x$. 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

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

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.