Science:Math Exam Resources/Courses/MATH100/December 2012/Question 06 (b)
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Question 06 (b) 

FullSolution Problems. In questions 511, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. 6. Let . Note that the domain of ƒ is the set of all nonzero real numbers; for example, . (b) Find the xcoordinates of the local maxima and local minima of . 
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 

Remember that local extrema can only occur at critical points (that are also points in the domain). Check the critical points from the previous part and determine if they are local maximums or local minimums (refer to part a for the necessary computations). 
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. As stated in the hint, local extrema can only occur at critical points that are also points in the domain. Based on our work in part a, we have two critical points, but only is in the domain. Thus, we only need to check if is a minimum or maximum. Here since we have a decreasing function left of 1 and an increasing function right of 1, we have that is a local minimum. 