Problem 5. (18 points) From Wikipedia: In computer architecture, Amdahl's law is a formula which gives the theoretical speedup in latency of the execution of a task at fixed workload that can be expected of a system whose resources are improved. The formula given is S = 1 (1 - x) + 2, Where . S is the theoretical speedup of the execution of the whole task . x is the proportion of the original task that benefits from improvements . y is the speedup of that part of the task that benefits from improvements Take the above formula to define a function S = f(x, y). (a) (6 points) Find formulas for fr, fy and show that x = 0, y = 1 is a critical point. (b) (6 points) Using the formulas below, classify the critical point in part (a) with the second derivative test. Show all work in your calculations. 2 fox = [ - 2+1 1 2x fxy = yz (2 - x+1 ) y2 (" - 2+ 1)" 2x2 2x fyy = y ( 2 -x+1) y3 2 -x+1)In context, it only makes sense to consider values of (any) where .7: is a proportion (0 1). The diagram below shows several contours for f (3:, y) in this domain. 0.0 0.2 0.4 0.6 0.8 1.0 (c) (6 points) Compute a Riemann sum approximation for \"h f (3:, y) dA, where R is the rectangle 0 S :c S 1, 1 g y g 2, using four equal subrectangles. Do not attempt to evaluate the double integral exactly. (The true value is ln(4) 1 + g m 1.20876, but you will only be graded on your methodology and presentation, not how close you come to this value.)