## j814wong 2 years ago Use the intermediate value theorem to show that the equation e^(-x)=x has at least one real solution.

1. asnaseer

@j814wong - do you know what the intermediate value theorem states?

2. j814wong

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.

3. satellite73

this is what you do consider $$e^{-x}-x$$ on the interval say $$[0,1]$$

4. satellite73

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

5. j814wong

What does the \ mean?