Sketch the graph of a mystery function given the following info: Step 1: Find the x-intercepts and y intercepts x intercept (0,0) x intercept (1,0) 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. Intervals (-op, 0.25) (0.25,1) (1, 00) Sign of f'(test value) + + f increasing f decreasing f increasing f increasing f decreasing Local Min (0.25, -1.7) 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 (-00,0.5) (0.5,1) (1, 00) Sign of f"(test value) + + f concave up Concave up Concave down Cocave up f concave down Inflection Point (1,0) Inflection Point (0.5, -1) 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. Mark axes off in 0.25 increments as shown below0.25 0.5 0.75 -0.25 -0.5 -0.75 -1 -1.25 -1.5 -1.75 -2