Science:Math Exam Resources/Courses/MATH100/December 2013/Question 08 (d)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 • Q10 (a) • Q10 (b) • Q11 •
Question 08 (d) 

Let . Sketch the graph of and indicate the inflection point(s) on your graph. (The results from parts (a), (b), and (c) may be useful.) 
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 

What are the critical numbers of ? What are the intervals of increase/decrease of ? How do these relate to the extrema of ? 
Hint 2 

What are the intervals of concavity of ? What is an inflection point, and how does it relate to concavity? 
Hint 3 

It may be useful to find the xintercept(s) of . In addition, note the behaviour of near . 
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. From parts (a), (b), and (c) we know the following about :
