Question

Use the Intermediate Value Theorem to show that cosx=x have at least a solution in [0,π]?

Answer 1

We have:

`cosx - x= 0`

Now let `y = cosx - x`. We see that `y(0) = cos(0) - 0 = 1` and `y(pi) = -1 - pi`

Since `y(pi) < 0 < y(0)`, and `y` is continuous, there must be a value of `x` in `[0, pi]` where `cosx -x = 0`.

Hopefully this helps!