Consider the data f(-2) = 6, f(-1) = 2, f(1) = 3, f(2)= 10, and assume that f is a smooth function. (a) Find p3(x), the cubic interpolating polynomial. Explain the method and formulas you use to find it. Give and estimate of the error p(x) - f(x) for x around x = = 0. (b) The data suggest that f has a minimum between x = -1 and x = 1. Find an approximate value for the location xmin of the minimum. (c) If in addition you know that f 0 (-2) = -1, construct an interpolating polynomial p(x) so that p 0 (-2) = -1. Explain the method and formulas you use to find it. Give and estimate of the error p(x) - f(x) for x around x = 0.