Write a code to compute a natural spline s(x) which interpolates a collection of given points (x0; y0); (x1; y1); : : : (xn; yn) where x0 < x1 < x2 < : : : < xn (do not assume they are equidistributed). your code should have a triadiagonal solver for the resulting linear system of equations (you're not allowed to use matlab's n operator to solve the linear system).

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)