Given that is function that's differentiable on the interval where .
1.) Prove has at most 1 fixed point on the interval . (ie., show there's at most 1 point where
2.) By giving specific examples, show it's possible that either has no fixed points or that has 1 fixed point on .
I thought f'(x) =! 1, but you have that f'(c) = 1..
I could see a contradiction if x_1 was strictly less than x_2, but it can also be equal, so perhaps I'm overlooking it. Then, if x_1 were equal to x_2, there'd be a contradiction. But you have the stipulation that it can be equal to it.
And to Jhevon: that was the exact question. I'm not sure if I can use a trivial example such as that, as this was a big question and I doubt it'd be that easy.