[awhig]

Originally Posted by Dragonfinity

Let there be two equations on the xy axis: f(x) = x ^12 and g(x) = 2 ^x. Both are continuous and defined for all x. I showed above that

for x = 1, f < g
for x = 2, f > g
for x = 100, f < g

Since f and g are continuous, there must be 2 intersection points to the right of the y-axis. [If you don't understand why this is true, consider the function h(x) = f(x) - g(x)]. You already agreed that there is 1 intersection point to the left of the y-axis. Hence, there are 3 intersection points.

You are making this more complicated than it is. From your profile, I see you are not a mathematician, so why are you arguing against this so hard? If you just don't understand, say so, but I get the impression that you are telling us we are wrong. Trust me, Matroid and I are not wrong on this. We know our stuff. I am just too lazy to do the algebraic solution again, but I will take the time to work it out again if it will help you understand. Alternatively, when I get home from work tonight, I will graph it on Mathematica and post the graph if you like.

You're kidding about the differential equation, right? Let y = x ^12 - 2 ^x and find the zeros of the function. What does a differential equation have anything to do with this problem?

It is unfortunate that you are taking me as though I am arguing.
I am just presenting my perspective. Though I do not say I am a scientist, but as far as Mathematics is concerened, I also did it . If you think I am challenging you, it is again unfortunate.