Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (b)
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Question 11 (b) |
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Consider the function
You are told that there is a critical point somewhere near the point .
(b) Use Newton’s Method to find a better approximation of the location of the critical point. Only one step is needed, i.e. you are given and asked to find . (Leave your answer as a simple fraction of integers.) |
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 |
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Recall that, in solving , the formula for the first step in Newton’s Method is |
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.
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Solution |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Recall from the solution for part (a) that We need to solve near . Using the Hint with in place of , we have Answer: the next approximation is . |