Problem 1-Consider the following function: (x)--3-1. Then complete part (a) by M

Question

Problem 1-Consider the following function: (x)--3-1. Then complete part (a) by MATLAB, and (b) and (c) by hand calculations. (a) Plot the function with an appropriate range of x such that all real roots are clearly visible. (b) Find the lowest root with bisection method. Start by choosing an appropriate bracket from observing the plot from part (a). Iterate twice. Clearly show bracket locations for each iteration. Evaluate function values and approximate relative percent errors. Generate an iteration table similar to the one that was used in lab handout. (c) Find the second lowest root with false position method. The rest is similar to (b). Iterate twice and generate an iteration table.

Explanation / Answer

a)

p=[1 0 -3 -1] % making matrix of polynomial

r=roots(p) % calulating roots

r1 = r(imag(r)==0); % check for real roots

r1 % displaying real roots

f = @(x) x.^3-3*x-1;   

x = -2:0.1:2; %interval [-2,2] well contained under 1.13 and -0.74

plot(x,f(x)) %plot the funtion

grid on

hold on

plot(r1,'bx') % plot real root as blue cross

b)

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