The solution in Problem 1 might look smooth, but it might not feel smooth because the piecewise

Question:

The solution in Problem 1 might look smooth, but it might not feel smooth because the piecewise defined function [consisting of L1(x) for x 100 doesn€™t have a continuous second derivative. So you decide to improve the design by using a quadratic function q(x) = ax2 + bx + c only on the interval 10
(a) Write a system of equations in 11 unknowns that ensure that the functions and their first two derivatives agree at the transition points.
(b) Solve the equations in part (a) with a computer algebra system to find formulas for q(x), g(x), and h(x).
(c) Plot L1, t, q, h, and L2, and compare with the plot in Problem 1(c).