Science:Math Exam Resources/Courses/MATH102/December 2016/Question A 05
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Question A 05 

An object is placed on the kitchen table at time t =0(t in minutes). Let A be the average rate of change of the temperature of the object over the interval . Let denote the temperature of the object at time t. Which of the following statements is true? (i) If the object is a pizza that was taken out of the oven, then . (ii) If the object is a bottle of milk that was taken out of the fridge, then . (iii) If the object is a pizza that was taken out of the oven, then . (iv) If the object is a bottle of milk that was taken out of the fridge, then . 
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 

The average rate of change is the slope of the secant line through the points and , whereas and represent the slope of the tangent line at the points and respectively. Recall that the (instantaneous) rate of change of the temperature of an object is given by , where is the ambient temperature and k is a positive constant. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Note that since we have . This will help us to determine the concavity and therefore, the comparison between slope of the tangent line and the slope of the secant line.
