How do you use the mean value theorem to find roots?

1 Answer
May 12, 2015

I don't believe the Mean Value Theorem can be used to find roots.

The mean value theorem tells us that under certain conditions,
(namely, #f# continuous on #[a,b]# and differentiable on #(a,b)#)
there is a value in a specific interval (namely #(a,b)# ) that solves a certain equation.
(#f'(x)=(f(b)-f (a))/(b-a)#)

The theorem gives no information on how to find a solution. It only asserts that a solution to a particular equation exists.