Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 29(a)
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Question 29(a) 

Let . (a) Let . Use three iterations of Newton's method to find and . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Recall that Newton's method uses the linear approximation of a function at to estimate a root of said function. The linear approximation of at is the line with equation

Hint 2 

Iteratively, set to be the intercept of the the linear approximation at . 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. As in the hint, the linear approximation to the function at is the line of points that satisfy the equation . The intercept of this line is
which we call . Since the derivative of is given by and was chosen to be 0, we have
