Hello!
This is the equation Im stuck with:
Im not sure where to start, because I cant take out any of the x values,
should i let 0.5x be a completely new vale like 'y' and but then i will still be stuck
Thank you!
Hello!
Thank you so much for the reply!!!
Yes i am asked to find the value of x and the answer is required to 3 s.f.
It might be better if i give you the context of the equation.
''''''''''''There are two equations g(x) and f(x), There are two values of x for which the gradient of f is equal to the gradient
of g. Find both these values of x. '''''''''"
So i've already found the derivative of the two equations and i've checked that its correct, and then i equated the two derivatives, but i dont know how to find x.
I was thinking that maybe it could be done by trig identities, lol but i dont know how though
anyways Thank you! !!
Hello appleseed
There are infinitely many solutions to the equationwhich is what I assume you meant. (You should have written 3/(3x+2) if you don't know how to write it using LaTeX.)
Have a look at the diagram I've attached, where I've plotted the graph of each side separately.
You won't be able to solve an equation like this to get exact answers. You'll have to use a numerical method - e.g. Newton-Raphson. Do you know how?
Grandad
Hello appleseedIf you've not had any practice with this method, this is not the easiest example to start with.
If you want to get a solution to the equationand you have a first approximation, , to the answer, then a second approximation, , is given byIn this case you'll have to let
So
From the graph, there's a solution close to . So with we get
... and so on.
The next approximation, , uses as the starting value:Repeating the process, to 4 d.p., I make the answer .
(to 2 d.p.)
The next positive solution is around . To 4 d.p., the solution converges very quickly to .
Grandad