Question

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

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

What does the \ mean?