16. [-/1 Points] DETAILS SCALCCC5 2.7.AE.001. MY NOTES ASK Y EXAMPLE 1 The graph of a function f is given to the left. Use it to sketch the graph of the derivative f. SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 5 we draw the tangent at P in the figure and estimate its slope to be about 3/2, sof' () = 1 . This allows us to plot the point P '( ) on the graph of f' directly beneath P. Repeating this procedure at several points, we get the lower graph shown in the figure. Notice that the tangents at A, B, and are horizontal, so the derivative is there and the graph of f ' crosses the x-axis at the points A', B', and C', directly beneath A, B, and C. Between A and B the tangents have -Select. slope, so f '(x) is -Select- there. But between B and C the tangents have -- Select--- | slope, so f '(x) is -Select-- > there. Select- negative PIS.IS) positive Video Example ) Need Help? Read it Sul Viewing Saved Work Revert to Last Response