Science:Math Exam Resources/Courses/MATH105/April 2014/Question 04 (a)
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Question 04 (a) 

Let . Find all critical points of and classify each as a local maximum, local minimum or saddle point. 
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! 
Hint 

Calculate the critical points. At a critical point and are equal to zero. Then use the second derivative test to check if the critical point is a maximum, minimum or saddle point. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Compute the derivatives:
Set and to find critical points:
From the first equality we get . Plugging this into the second equality, we get . Solving it gives and . This yields the critical points , and . For , , and , so we have a saddle point because . For , , , and (and thus it could be a local max or local min). Then, because , we conclude it is a local minimum. 