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# Newtons Method using Mathematica

If its possible to answer these three questions using mathematica 5 if matlab looks similar, or the commands are similar then i guess matlab is fine... if its at all possible for mathetmatica it would be much appreciated

Using Newtons Method

1. Plot f(x) = a on the interval - 3 &#8804; x &#8804; 3.
a) Use NewtonGraph[ ] starting with a = 1.5 and n = 3. Obtain a printout of this command and on your
printout, explain why it does not work.
b) There appears to be one root near x = 0.5 and another root near x = 2.7. Try using NewtonTable[ ]
starting with a = 1.7 and n = 8. On your printout, indicate if this yields either of the positive roots and
explain why it gives the root that it does.
c) Use NewtonTable[ ] to find all the roots of f(x) to 8 significant figures and clearly indicate these values

3. Obtain a printout that shows the two functions f(x) = 1 + 3x - a and g(x) = 5 - 2a. Use NewtonTable[ ] to find the x-coordinates, 6 significant figures, of all the points of intersection for these two functions. On your printout indicate the x and y coordinates, 6 significant figures, of all the points of intersection for these two functions. (HINT: if f(x) = g(x), then f(x) - g(x) = 0)

8. write two paragraphs clearly explaining what the purpose of this lab is.

#### Solution Preview

I am attaching a program here. May be this will serve the purpose for you. But I am unable to give a clear answer as your question is a bit confusing.

Here are my ...

#### Solution Summary

Newtons method for finding the root is implemented using Mathematica

\$2.19