Science:Math Exam Resources/Courses/MATH110/April 2013/Question 02 (c)
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Question 02 (c) 

Sketch a single function satisfying all of the listed criteria.

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 

Recall that at an inflection point the function switches concavity (but does not necessarily switch from increasing to decreasing or decreasing to increasing); at a critical point, the slope of the function is zero (often a maximum or minimum) or the derivative doesn't exist. 
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. Your drawing should have a function that changes concavity at x = 1. Critical points are where we find a minimum, maximum, or a "corner" where the derivative does not exist. Your graph should have one of these features at x = 2. In our example below the function switches from concave up to concave down at x = 1 and has a maximum at x = 2. 