Question

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

Answer 1

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.