Science:Math Exam Resources/Courses/MATH102/December 2019/Question 05 (b)
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Question 05 (b) 

For this question, let
You may use the following facts without proving them: (b) Does the function from (a) give an overestimate or an underestimate of for values of close to (but different from) 10? Why? 
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 

Think about the concavity of . For example, if it is concave up, its graph will lie on top of its tangent line. 
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Solution 

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Therefore, the tangent line as a linear approximation is an overestimate of . 