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(@function,xo) xo is an initial guess Note: xo could be a range (eg. [0 3]) 


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Definition
10 values for the 5th column 


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solve for the following using MATLAB: y= x^5 + 3x^3  2*x^2 + 3 when y = 0, x = ? 

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Write a short MATLAB script (program) that uses a while loop to divide the variable x by 2 until the value of x is less than 1.0e6. The program should also count the number of times x was divided by 2. Before starting the while loop set x = 1. 

Definition
x = 1; i = 0; while x >=1e6 x = x/2; i = i + 1; end



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(7 pts) Write a MATLAB function mfile called prob5 that requires two input vectors x and y (with the same number of elements) and outputs two scalar values a and b, where a is the intercept and b is the slope from linear leastsquares regression. Use the MATLAB polyfit command to determine a and b inside your function 

Definition
function [a, b] = prob5(x, y) p = polyfit(x, y, 1); b = p(1); a = p(2);



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(6 pts) Use your function from question 5) above to fit data given in vectors x and y to a powerlaw of the form: Assume that x and y have been entered already in the MATLAB command window. Just write out the required statements to compute A and B using your function prob5. 

Definition
[a, b] = prob5(log10(x), log10(y)) B = b A = 10^a



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If x = [1 2 3 4] and y = [0 1 4 9]. Write a MATLAB program that will determine the coefficients for polynomial interpolation (i.e., the polynomial that passes through the data points exactly). 

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