Science:Math Exam Resources/Courses/MATH104/December 2011/Question 02 (g)
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Question 02 (g) 

Draw the graph of ƒ(x) on the graph provided. Accurately place all critical points and inflection points, indicate all asymptotes, and make sure your graph correctly shows where ƒ(x) is increasing and decreasing and correctly shows its concavity. 
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 

You don't even need to use the expression for ; the answers from parts a  f should be sufficient to draw the graph. 
Hint 2 

Try going step by step.

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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Following the order given in Hint 2, we first draw the asymptotes. We then draw the maxima and minima. We draw the inflection point. Finally, we use information about where the function is increasing and decreasing, as well as its concavity, to connect these points and finish the graph.
