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MTH 121 - Summer - 2005
Essex County College - Division of Mathematics and Physics
Bonus Question #5 1 - Printed June 7, 2005
Name:
Signature:
The following question is worth ten points total, and will be added to your second exam score.
Only correct answers will be accepted. Due 06/16/2005.2
1. Use Newton's method to find the absolute minimum value of the function
f (x) = x2 + sinx
correct to six decimal places. Please trust the given graph, as it will help you determine
if your final boxed answer is reasonable.
Figure 1: Graph of f (x) = x2 + sinx.
Solution: First, you need to find the first derivative.
fprime (x) = 2x + cosx
Now, you'll need to find where this derivative is zero. Looking at the graph, a good starting
guess3 is x1 = ?0.43. Using Newton's method to find this solution to fprime (x) = 0, we have
xn+1 = xn ? f
prime (xn)
fprimeprime (xn) = xn ?
2xn + cosxn
2?sinxn .
1This document was prepared by Ron Bannon using LATEX2?. Source and pdf are available by emailing a
request ...

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