Graded Problem 03 Directions:

• Use a ruler to measure the distance between tick-marks on the x and y axes then use that information to scale the distances everywhere else in the picture. In other words, if you state the length of something to be 1.5, it should be 1.5 tick-marks as shown on the axes of the graph.
• Explain how you made each estimation and show where you made each estimate on the graph. Include the graph with all your own sketches as part of the GP. You may want to copy the picture and use it various times to illustrate your answers to each question individually.
• Write clearly in sentences from the left edge of your paper to the right edge of your paper as you explain your methods.

1. The contours of a function are graphed in the diagram below along with an elliptical constraint :
2. Estimate. Explain how you made your estimation and show your work.
3. Estimate
4. Sketch on the graph as best as possible. Explain how you made your estimation and show your work.
5. Use the graph to estimate in the direction of .Explain how you made your estimation and show your work.
6. How many local extrema do you expect to find along the constraint? Explain your reasoning.
7. Show the locations of the local extrema on the constraint and include estimates of their (x, y, z) coordinates. Remember not all contours of the function are shown. For instance between contour z = 1 and z = 3 there must be contours z = 1.5 and z = 2.6, but they are not shown.
8. Classify each of the extrema you found in part (f) as local min/maxeither.Explain how you made your decisions.
9. Estimate the global extrema for the region less than or equal to the constraint? What are the locations and what are their values? Explain your reasoning.