Question

How do you use the intermediate value theorem to show that there is a root of the equation `e^(-x^2)` over the interval (0,1)?

Answer 1

You can't.

Explanation:

`e^(-x^2)` is not an equation, it is a function.

We can ask whether the function has a zero in `(0,1)`.

It does not. for any real `t`, e^t > 0#, so

`e^(-x^2) > 0` for all real `x`.