Science:Math Exam Resources/Courses/MATH102/December 2016/Question A 06
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Question A 06 

The graphs below represent the position, velocity and acceleration of a child swinging on a swing. Identify the correct relationships between these functions. (i) (ii) (iii) (iv) (v) (vi) 
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 

Start with the fact that where a differentiable function has a (local) max/min (zero slope) its derivative must become zero (intersects xaxis). The same reasoning will help you determine which one is the second derivative as is the derivative of the derivative. 
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. At the points where has a min/max (slope of tangent line =0), must be equal to zero, i.e. intersects xaxis. This fact eliminates the option of , because if so, we then see that at its maximum point neither nor vanishes.
Answer: 