The Maximum Value of a Function This project describes a simple example of a function with a maximum value that depends on two equation coefficients. We will see that maximum values can depend on several factors other than the independent variable x. 1. Consider the graph in Figure 1 of the function y = sinx + cos x. Describe its overall shape. Is it periodic? How do you know? y sinx + Cosx Figure 1 The graph of y = sinx + cos x. Using any graphing device, estimate the x - and y -values of the maximum point for the graph (the first such point where x > 0). It may be helpful to express the x -value as a multiple of TT. Prepared by : Reviewed by: Verified by: Approved by: localucag Dr. ucag man M. Norman | . Aleta or Teachers Dep wentDead inte Dean Dean Day Date : 30June 2020 Date : 30 Jun 2020 Date :30 JUNE 2020 AMA INTERNATIONAL UNIVERSITY - BAHRAIN Salmabad, Kingdom of Bahrain COLLEGE OF ENGINEERING #1 Special Project 1st Tri, 2nd Tri, X 3rd Tri, SY 2019-2020 PRELIM, _ MIDTERM, X FINAL MATH 406 - Differential Calculus with Analytic Geometry 2. Now consider other graphs of the form y = Asinx + Boos x for various values of A and B. Sketch the graph when A = 2 and B = 1, and find the x - and y-values for the maximum point. (Remember to express the x-value as a multiple of TT, if possible.) Has it moved? 3. Repeat for A = 1, B = 2. Is there any relationship to what you found in part (2)? 4. Complete the following table, adding a few choices of your own for A and B: B X 0 5. Try to figure out the formula for the y-values. 6. The formula for the x -values is a little harder. The most helpful points from the table are (1, 1), (1, v3), (V3,1). (Hint: Consider inverse trigonometric functions.) 7. If you found formulas for parts (5) and (6), show that they work together. That is, substitute the x -value formula you found into y = Asinx + Bcos x and simplify it to arrive at the y-value formula you found