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3.3 (6 pts) Do your work in a file HW3_3.m. Polynomial interpolation is not perfect, and higher- order polynomials may not always give us the most accurate results. Consider the following data, which were generated from the function f(x) = sin? x: 0.0000 0.7500 1.5000 2.2500 3.0000 f(x) 0.0000 0.4646 0.9950 0.6054 0.0199 a. Plot these five data points, along with the original function f. b. Use an interpolating polynomial of order 4 and the best possible interpolating polynomial(s) of order 3 to determine the values of f(x) at the following points. Also calculate the error of these interpolations with respect to the TRUE value of f. (You are calculating a total of 4 values and 4 errors; print these to the command window.) i. x = 1.7 ii. x = 0.2 c. Plot the polynomials over their valid ranges (i.e., avoid extrapolation!). Ensure your plot is properly labeled, including a legend