Question: The function f(x) = ex has the properties
F'(x) = f(x) and f(0) = 1.
Explain why f(x) is the only function with both these properties. [Assume g'(x) = g(x), and g(0) = 1, for some function g(x). Define h(x) = g(x)/ex, and compute h'(x). Then use the fact that a function with a derivative of 0 must be a constant function.]