Problem 1: Analyze and sketch the graph of a mystery function given the following info: Step 1: Find the x-intercepts and y intercepts x intercept (4,0) x intercept {1, ll) 3.- intercept {0, -2) Step 2: Find '5 ' and set it equal to [l to nd the critical numbers. The critical numbers are where x]: 0 and when: x] is undened. 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 er neither. Find v values of each max er min. Intervals (-00, -1) (-1,0) (0,1 ) (1, 00) Sign of f'(test value) + + f increasing f decreasing f decreasing f increasing f increasing f decreasing Local Min (0, -2) 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 Intervals (-00,-1) (-1,1) (1, 00) Sign of f"(test value) + f concave up Concave down Concave up Concave down f concave down Inflection Point (-1,0) Inflection Point (1,0) Step 4: Use the above information to sketch the graph of f. a. List all points with descriptions (done) b. Find the range of x coordinates and range of y coordinates to figure out how to label axes. c. Plot all points with a description next to them Now connect the points by looking at the concavity of f and where f is increasing and decreasing