All results must be justified

1. (10 marks) Let f be a function with the property that f(0) = 1, f'(0) = 1, and f(a + b) = f (a) f (b) for all real numbers a and I). Use the denition of the derivative as a limit to show that f'(:c) = f(3:) for all 3:, and then deduce that f(:1:) = em