1. Suppose you are constructing an interpolating polynomial for a function on an interval [a, b]. (a) (6 points) Explain under what circumstances and why you might want to use Chebyshev points to form the interpolating polynomial of degree n or less for n + 1 points. (b) (6 points) Why might you not be able to use Chebyshev points? In these cases, give an alternative approach to address a situation in which Chebyshev points would have been desired. (e) (6 points) If you are able to use Chebyshev points, of the forms we have studied, what polynomial basis would you choose to construct the polynomial? Justify your answer with specific reasons. 1. Suppose you are constructing an interpolating polynomial for a function on an interval [a, b]. (a) (6 points) Explain under what circumstances and why you might want to use Chebyshev points to form the interpolating polynomial of degree n or less for n + 1 points. (b) (6 points) Why might you not be able to use Chebyshev points? In these cases, give an alternative approach to address a situation in which Chebyshev points would have been desired. (e) (6 points) If you are able to use Chebyshev points, of the forms we have studied, what polynomial basis would you choose to construct the polynomial? Justify your answer with specific reasons