The following is false. Show a counterexample and prove the correct statement. If f(x) is
differentiable on a, possibly infinite, interval (a,b) and if limx->b f'(x)=infinity, then f(x) is NOT
uniformly continuous on (a,b).
Solution
the derivative of a uniform continuous distribution should be 0. because the height
of the distribution is a flat line between the bounds (a,b). the distribution of a uniform continuous
variable looks like a rectangle. If the derivative of the function was infinity it would probably be
an exponential distribution.