MATH105 April 2012
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Question 07 (b)
(b) Classify each critical point you found in part (a) as a local maximum, a local minimum, or a saddle point of ƒ(x,y).
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Remember that the critical points are (0,0) and (e-1,-1). To classify them, use the second derivative test.
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To classify the critical points, we use the second derivative test.
From , we compute:
From , we find:
- At (0,0), we find . As , we have a saddle point.
- At , we find , so there is either a local maximum or local minimum. From , it must be a local minimum.
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