At what value(s) of $x$ does $ \cos(x) = 7x$? For some reason, this question was posed to me on a calculus quiz, and I have completely drawn a blank on how to solve this problem.
If someone could explain how to solve this problem, it would be greatly appreciated.
Thanks.
At what value(s) of $x$ does $\cos(x) = 7x$?

I will post an alternative iterative method.
Define a recurrence relation so that $a_0 = 1$ and $a_n = \dfrac{\cos(a_{n-1})}{7}$.
The solution to the problem is:
$$x = \lim_{n\to\infty} a_n.$$
The convergences of this series requires other math (Lipschitz constant satisfying certain conditions, etc.).
This may not work on a Ti-84 because of a lack of precision. 
