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Mathematics 161 Laboratory 6 October 8, 1992
Name: _____________________________ Lab Partner: ___________________________
Consulted with: ____________________________________________________________
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© Lafayette College, 1994
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NewtonÕs Method for Finding Roots
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In this laboratory you will use Newton's method to solve some equations and you will investigate some of the strengths and weaknesses of that method for approximating solutions of equations.
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Recall that if f(x) is a differentiable function, Newton's method uses the tangent line approximation to the graph of f to estimate the solutions of the equation f(x) = 0. (Solutions to this equation are called roots of f.) To get started, we make an initial estimate, x0, to a root and then generate new estimates using the x-intercept of the line tangent to the graph at the old estimate.
;[s]
20:0,0;15,1;16,0;17,1;18,0;118,1;119,0;162,1;163,0;164,1;165,0;212,1;217,0;221,1;222,0;271,1;272,2;273,0;327,1;328,0;393,-1;
3:10,14,10,AGaramond,0,12,0,0,0;9,14,10,AGaramond,2,12,0,0,0;1,17,10,AGaramond,64,9,0,0,0;
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Part 0: A Demonstration
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Preliminaries
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As in preceding labs, we will use some special commands contained in the "DerivativeGraphics" package; recall, we input the package as follows:
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