Science:Math Exam Resources/Courses/MATH100/December 2010/Question 01 (l)
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Question 01 (l) 

Find the absolute maximum value of 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Maximum values can only occur at the endpoints or critical points. Try all these values and see which is biggest. 
Hint 2 

To take the derivative, use the product rule. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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 first take the derivative to see that
Setting this to zero, we see that the function is zero whenever (the exponential function is always bigger than 0) and on our interval , this occurs at and at . Checking the endpoints and values at the critical points, we have
Hence, our function obtains its absolute maximum at and the value is . 