Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 25
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Question 25 

Let . Find all the critical points. Your answer(s) should include both  and  values, and be written in the form . 
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 

Critical points here are pairs that satisfy both and . 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We compute the partial derivatives and set them equal to 0:
We now solve for and . Let's start with the second equation. If the point satisfies , then either or .
The final list of critical points is . 