Science:Math Exam Resources/Courses/MATH110/April 2013/Question 01 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 (a) • Q9 (b) •
Question 01 (b) 

Determine whether the following statement is true or false. If it is true, provide justification. If it is false, provide a counterexample. (b) If ƒ has no critical points, then ƒ has no inflection points. 
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 

Recall the definition of critical point and inflection point. Recall how critical points and inflection points can be found using the graph. 
Hint 2 

What function do you know which graph has an inflection point? Try to think of at least one example. 
Hint 3 

What trigonometric function has an inflection point on its graph? 
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 1 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. This statement is false. Consider, for example, the graph of for π/2 < x < π/2. Nowhere do we have , but still the curve switches from concave down to concave up. 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The statement is false. Two more examples are , , and , . The argument is the same as in solution 1. 