(a) (b) Figure I The slope of a curve may be estimated by zooming in on the graph using a graphing utility until it appears linear. Suppose we wish to estimate the slope of the curve y = J; at (4, 2). a. Plot the graph of y = J; using the window [0,8] x [0,4] (Figure 2a). Does the graph appear to be nearly linear in this graphing window? b. Now zoom in by changing the graphing window to [3,5] x[1.5, 2.5] (Figure 2b). (If you are using a graphing calculator, the new window can be obtained automatically by using the zoom command, after rst setting the x and y zoom factors to 4.) Does the graph appear to be nearly linear near (4, 2) in this new graphing window? c. Two points on the Curve, (3.5063291,1.8725195) and (449367012. 1 19828) , were obtained using the 0. Two points on the curve, (3.5063291,1.8725195) and (4.4936709,2.119828) , were obtained using the trace command on a graphing calculator (Figure 2b). The slope between these points is 2.1198281.8725195 =02504791147- 1 4.4936709 3.5063291 ( ) Find two other points on the curve, within the window [3,5] X [15,25] and calculate the slope of the line joining these points. Approximate your coordinates with eight digits of accuracy. Is your answer close to the slope given in (1)? Explain. d. Zoom in again by graphing the function using the window [375,425] x [1.87 5,2.125] Locate two points on the curve in this new window and compute the slope of the curve again with eight digits of accuracy. e. Make a reasonable estimate of the slope of the curve at (4, 2) based upon your work in parts (c) and (d). f. Using the slope estimate in part (e), determine the equation of the line tangent to the curve at (4, 2). Graph the function y = J; and tangent line using the window [0, 8] X [0,4] . y d {4.4936709.2.119828) (3.5063291,1.8725195) (b)