solving 2tanx+x=0

[sssalsa]

need 2 find the turning point of the graph f(x)=cosx-xsinx so i differentiatied this and got f'(x)=-2sinx-xcosx
so i made this equal to 0 and worked my way down as follows:

0=-2sinx-xcosx
2sinx=-xcosx
2tanx=-x
2tanx+x=0

i dont kno where to go from here, any ideas.

[krtxmrtz]

The trivial solution is, obviously, x = 0.
The tan(x) plot vs x has infinite branches and there's one solution to your equation for each branch (plot both 2tan(x) and -x and you'll see both curves have infinite interceptions). If you need to find any of these, other than x = 0, then you must solve the equation by numerical methods as it can't be solved analytically.

[Guv]

The Newton iterative method should work. To find a zero of F(x), iterate the following.

NextX = X - F(X) / F'(X)

Guess at an initail value, computer NextX. then use NextX to compute another value. This usually converges to a correct value.