A Natural Cubic Spline S on $[0,2]$ is defined by:
S(x)= $S_0(x)=1+2x-x^3 \to 0 \leq x < 1 $ $S_1(x)=2+b(x-1)+c(x-1)^2+d(x-1)^3 \to 1 \leq x \leq 2$
Find b,c and d
This question seems simple I am just not sure how to go about it. Can someone please guide me as to how to find the solution