4. The goal of this problem is for you to show that n xb-1e-dx - 0 1 ebn1-b I n (1)* de dx for all real numbers 0 as - f(c) = e (1 ) e-c - and factor out the common factor of e-c to obtain ce f(c) = n (d) Use Calculus 1 techniques to show that the function h defined by h(x)=xe- has a maximum value of e- at x = 1. Conclude from this that f(c) n Deduce that - -(1-2)" e- n for all x in [0, n], due to the definitions of f and c. (e) Multiply both sides of the final inequality from part (d) by 2b-1 and integrate from a to n. Take the limit as a 0+ and rearrange to conclude that S e-1 n xb-e-dx n b Lab-1 (12)" dr - dx for all real numbers 0 1. Rewrite the second term on the left side as 1-6 to conclude. What exponential property did you use