1. Let f(x) = (5 x)e" 5. a. Plot f(x) for x between 0 and 5 b. Write a bisection routine to find a root of f(x) in the interval [4, 5], accurate to six decimal places (i.e., find an interval of width at most 10-6 that contains the root, so that the midpoint of this interval is within 5 x 10-7 of the root). At each step, print out the endpoints of the smallest interval known to contain the root. c. Without running the code further, answer the following: How many steps would be required to reduce the size of the interval of this interval to 10-12? Explain your