Finding Solutions Using the Intermediate Value Theorem

[Vashti]

Homework Statement

Show that the equation e^x = x + 2 had exactly two solutions. Explain your reasoning.

Homework Equations

Okay so I guess I'm using the intermediate value theorum and proving that f(a)f(b) < 0 we can find a c and d such that f(c) = 0 and f(d) = 0 so that by collorary it's true. This is an issue because I don't have boundaries for my function...

The Attempt at a Solution

create a function: f(x) = e^x - x - 2
and that's about as far as I got. I'm assuming I arbitarily select an interval and use that? Are there rule that I should follow though?

 

[rock.freak667]

I would believe you should select some values and check for a sign change...