Sketch the graph of the MYSTERY FUNCTION given the following info: Step 1: The x-intercepts and y intercepts x intercept (0,0) x intercept (-2,0) Step 2: Find f ' and set it equal to 0 to find the critical numbers. The critical numbers are where f'(x)= 0 and where f'(x) is undefined. Use the critical points from to set up intervals. Then set up a chart which indicates where your function is increasing and decreasing. Use the chart to classify each critical point as a relative maximum, relative minimum or neither. Find y values of each max or min. HERE the chart is done for you. Intervals (-,2) (2,0.5 ) (0.5, ) Sign of f'(test value) - f increasing f decreasing f increasing f increasing f decreasing Local Max (0.5, 6.75) Step 3: Find f " and set it equal to zero. Form intervals using these points. Set up chart and use f '' to determine the concavity in these intervals and whether the point is an inflection point. Find the y values of any points of inflection. HERE the chart is done for you. Intervals (-,2) (2,1) (1, ) Sign of f''(test value) f concave up f