Science:Math Exam Resources/Courses/MATH102/December 2015/Question 13
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Question 13 

What is the absolute minimum of the function on the interval ? 
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 

First find the critical points. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Note that all local minimums occur at critical points, so that critical points are the candidates of the point which achieves absolute minimum. Therefore, we first find the critical points. Since , the critical points are . (i.e, ) Since is the only point in the given interval , we compare the function value at this point with the ones at the boundary points, to find the absolute minimum; , , and . This implies that we have the absolute minimum . 