Exercise 6. Find cubic polynomials S0(x) and S1(x), such that S0(0)=0,S0(1)=1,S1(1)=1,S1(2)=1,S0(1)=S1(1),S0(1)=S1(1), plus two boundary conditions for each of the following spline types. For each type, graph the spline (on the interval [0,2] ) by a computer. (Graph S0 on [0,1] and S1 on [1,2], in the same coordinate plane. So, you are producing two graphs, one for Part a, and one for Part b.) (a) Natural: S0(0)=0,S1(2)=0. (b) Clamped: S0(0)=1,S1(2)=0. Exercise 6. Find cubic polynomials S0(x) and S1(x), such that S0(0)=0,S0(1)=1,S1(1)=1,S1(2)=1,S0(1)=S1(1),S0(1)=S1(1), plus two boundary conditions for each of the following spline types. For each type, graph the spline (on the interval [0,2] ) by a computer. (Graph S0 on [0,1] and S1 on [1,2], in the same coordinate plane. So, you are producing two graphs, one for Part a, and one for Part b.) (a) Natural: S0(0)=0,S1(2)=0. (b) Clamped: S0(0)=1,S1(2)=0