Here's the question you clicked on:
j814wong
Use the intermediate value theorem to show that the equation e^(-x)=x has at least one real solution.
@j814wong - do you know what the intermediate value theorem states?
Sorry for the late reply. Yes. If f is continuous on a closed interval [a,b] and k is any number between f(a) and f(b), inclusive, then there is at least one number x in the interval [a,b] such that f(x)=k That's the formal definition as opposed to the one I'd give on teh spot.
this is what you do consider \(e^{-x}-x\) on the interval say \([0,1]\)
at \(x=0\) you get 1 at \(x=1\) you get \(\frac{1}{e}-1\) since 1 is positive, and \(\frac{1}{e}-1\) is negative, by the ivt it must be zero somewhere in between 0 and 1