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Homework Statement f(x) = {x, x rational, 0, x irrational g(x) = {x^2, x rational, 0, x irrational Show that f(x) is not differentiable at 0. Show that g(x) is differentiable at 0 Homework Equations f'(x) = lim(h->0) f(x+h) - f(x)/h I suppose The Attempt at a Solution Just...

The question is from http://www.math.toronto.edu/~joel/137/assignments/a4.pdf Question 5 on the last page. I do believe I copied it word for word. I think I understand what you're saying union. In other words I don't have to show that f(x) = 1-x, but that there must be at least one x...

Homework Statement Suppose f (x) is a continuous function on [0;1], and 0 <= f(x) <= 1 for all x any [0;1]. (a)Show that f (x)= 1 - x for some number x. (b)Prove the more general statement: Suppose g is continuous on [0,1] and g(0)= 1, g(1)= 0,then f(x)= g(x) for some number x...