Science:Math Exam Resources/Courses/MATH104/December 2013/Question 06 (c)
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Question 06 (c) 

Is your approximation for too large or too small? Explain. Use the information together with the error bound you found in part (b) to construct the smallest interval you can guarantee contains the true value of 
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 

A linear approximation to a function has a concavity of 0 for all but the function does not have a concavity of zero. Use this fact to determine if the linear approximation lies above or below the function at . 
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. Since the second derivative is negative on , the function is concave down there. Thus, the tangent line is an over estimate of the function and the true value must lie in the interval 