Answer Happy

Question #4 In 1701, Isaac Newton (one of the co-founders of Calculus) studied the shape and graphical properties of a specific type of rational function of the form y = abx x2 + a2 , which became known as Newton's Serpentine. For this type of curve, the following properties can be determined in general: - It has a maximum point where x =a and a minimum point where x = -a - The maximum and minimum values of the function are b b and 12 - 2 - Points of inflection occur where x = 3 a, -3 a, 0 Using an a-value equal to the month number that you were born, and a b-value equal to the day number of the month that you were born (i.e., September 30th would have a=9 and b=30), verify the above listed properties for your associated function using the Curve Sketching Algorithm that was used in class. Additionally, identify any other pertinent graphical properties for your function (.e., intercepts, asymptotes, etc.) that come about from using the algorithm.