Answer: COMPUTER EXPLORATIONSIn Exercise, you will explore

Chapter 14, Problem 71E

(choose chapter or problem)

Problem 71E

COMPUTER EXPLORATIONS

In Exercise, you will explore functions to identify their local extrema. Use a CAS to perform the following steps:

a. Plot the function over the given rectangle.

b. Plot some level curves in the rectangle.

c. Calculate the function’s first partial derivatives and use the CAS equation solver to find the critical points. How do the critical points relate to the level curves plotted in part (b)? Which critical points, if any, appear to give a saddle point? Give reasons for your answer.

d. Calculate the function’s second partial derivatives and find the discriminant

e. Using the max-min tests, classify the critical points found in part (c). Are your findings consistent with your discussion in part (c)?