AP Calculus Page 1 of 1 Assignment: Comparing Calculator Derivatives to Real Ones User Name: Instructor: Date: (print clearly) Directions First, write which model of calculator you are using for this assignment. Now take a look at the following three functions: x) =X2+ 2X- 1 500 six} = X k(x) = Ix - 2| , 1:0 For each function, do the following: 1. Compute the derivative {that is, the derivative function) by evaluating the limit for f(-+h}-f(xl example, 1in1,,_,,:I ' h you'll have to compute the limit differently depending on whether x r: 2 or x > 2, and you'll end up with a piecewise function for the derivative. Since the graph of x) is made of straight lines, you can also find its derivative by looking at the actual slopes.) . Show your work. (Notice that for the function x), 2. Graph the derivative, for}, on your calculator by assigning it to the function Y1. Draw the graphs that you create on your calculator. Make sure to label and submit them along with the rest of the assignment. 3. Graph the function Y2 = nDerivf'criginal function",X,X). By doing this, you're having the calculator evaluate the derivative numerically at each point and graph the results. 4. Discuss how the two graphs are the same or different. Zoom in and out to find places where the graphs differ. A good idea is to set Y3 = Y2 - Y1, deselect (but don't erase) the functions Y1 and Y2, and look at the graph of Y3. Discuss what this illustrates, and see if it helps you in your comparison. Discuss the things you did in order to compare the two graphs. After you've done these things for each of the three functions, make a final comment about when the graph made by nDen'v was most or least accurate. Try to come up with a general comment, such as \"nDen'v seems to work best near points where the derivative is near 0." (Note: This is just an example, not necessarily a true statement.)