[-/1 Points] DETAILS SCALCCC5 2.7.054. MY NO 16. [-/1 Points] DETAILS SCALCCC5 2.7.AE.001. MY NOTES ASK YOUR TEACHER The figure shows graphs of f, f', f", and f". Identify each curve, and explain your choice: Figure Description EXAMPLE 1 The graph of a function fis given to the left. Use it to sketch the graph of the derivative f'. abcd 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, so f "( 1) =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 PIS.IS) 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-- v there. -Select- negative positive f ? v f' ? v Video Example () Need Help? Read It Need Help? Read It Submit Answer Submit