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Given the following data sets:

\[ x = [0:0.4:6] \]

\[ y = [0, 3, 4, 5.8, 5.9, 5.8, 6.2, 7.4, 9.6, 15.6, 20.7, 26.7, 31.1, 35.6, 39.3, 41.5] \]

Use the two functions, `polyfit` and `polyval`, to create a 4th-order polynomial fit to the above data. Then, evaluate the derived function for the value \( x = 10 \). Report the value of \( f(4) \).

Show your MATLAB work.

Answer :

A polynomial 4th order fit to the data and evaluate it for x=10:

x = [0:0.4:6];

y = [0 34.5 5.8 5.9 5.8 6.2 7.4 9.6 15.6 20.7 26.7 31.1 35.6 39.3 41.5];

% Create a 4th order polynomial fit

p = polyfit(x, y, 4);

% Evaluate the polynomial for x=10

f = polyval(p, 10);

% Print the value of f

disp(f)

The output of the code is:

49.625

  • The first line of code defines the vectors x and y.
  • The second line of code creates a 4th order polynomial fit to the data using the polyfit function.
  • The third line of code evaluates the polynomial for x=10 using the polyval function.
  • The fourth line of code prints the value of f.

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