Question

(4) (Interpolating polynomials) Say we want to find a polynomial f(x) of degree 3, satisfying some interpolation conditions. In each case below, write a system of linear equations whose solutions are (ao, a1, a2, az). You don't need to solve. (a) We want f(x) to pass through the points(1,-1), (1, 2), (2,1) and (3,5). (b) We want f(x) to pass through (1,0) with derivative +2 and (2,3) with derivative-1 (c) (Discuss) What if we had more than four points to consider? Fewer? (d) (Discuss) Can we still use linear algebra if f(x) is another kind of function, such as (x)asin(x) + bcos(r)? f(x) - aeb?

I am confused about how to solve (b) (c) (d)

Answer 1