Science:Math Exam Resources/Courses/MATH101/April 2012/Question 01 (e)
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Question 01 (e) 

ShortAnswer Question. Show all your work, simplify your answer as much as possible. A function is always positive and satisfies for all x and also . Find this function. 
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 

Convert this problem to a [separable] differential equation and solve. 
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. Let . Then the problem becomes Separating and solving yields When we know that and plugging this information in yields Continuing to simplify yields Since y is a positive function, we know that the final answer is as required. 