EXERCISE 1: 5 Given the following function: y = I? x3 + 4 a) Find the extreme points, and prove which ones of them are MAXIMA and MINIMA (10 points} b) Find the inflection points (5 points) C) Draw the graph of the function (5 points} EXERCISE 2: Suppose that the revenues function of a certain product in function of the thousands of units sold yearly {x} is: R(x) = -x2 +10): -3 And the function of costs is: (200 = x3 - 3x2 -x +12 a) What is the function of prots? (5 points) b) Is there a sales level that maximizes profit? If so, what are the points of maximum profit? (5 points}l c) What should be the sales that give the largest yearly revenue? (5 points) cl) What should be the sales that give the minimum yearly cost? (5 points) EXERCISE 3: Find the following integrations (20 points) a. S (5+ x5 +5vx -5x ) dx (4 points) b. f sin(3x) dx (4 points) c. fe5x+2 dx (4 points) 10x+7 d. J 5x2+7x-1 dx (4 points) e. J -xsinx . dx (4 points)EXERCISE 4: (20 points} Draw and find the area surrounded by the graph generated by: - The function f(x) = x3 + 2x2 + 6x 5, - The Xaxis, and - The points X=1 and X=3 EXERCISE 5: (20 points} Draw and find the area generated by: - The functions f(x) = 3x2 x + 7, and 9ij = 2x + 13 - Between the points where they intercept