Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 01
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QB 1 • QB 2 • QB 3(a) • QB 3(b) • QB 3(c) • QB 4(a) • QB 4(b) • QB 4(c) • QB 5(a) • QB 5(b) • QB 6(a) • QB 6(b) • QB 7(a) • QB 7(b) • QB 7(c) • QB 8 •
Question B 01 

The zeros of the quartic function are labeled from to , running left to right. Using Newton’s method, starting at the points and (black dots), which zero will be found? Several relevant tangent lines have been provided (dashed lines). 
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 

Using Newton's method, find the tangent line at each of the given points , then find the points where each tangent line crosses the xaxis, the closest root to this point is the root that is approximated. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The tangent line at crosses the xaxis at a point close to , so starting at will approximate . At the tangent line again crosses the xaxis at a point close to , so is used to approximate too. At the tangent line crosses the xaxis at a point close to , this means that is a starting point to approximate . The tangent line at crosses the xaxis at a point close to , so starting at will approximate . Answer: . 