3. (a) Verify that the Hermite cubics (page 73 of text) determine a Hermite interpolation of a sufficiently smooth function f(x) on the interval (a, ). That is, show that they satisfy Definition 1 in Lecture 6. (b) Construct the piecewise cubic Hermite interpolation of the func- tion f in problem 2 on the interval (-4, 4] by fitting a cubic Her- mite polynomial on each subinterval (ak, ak+1), k = 0,1,2, ...39 using only the end points of the interval for interpolation. (c) Plot the interpolant from Part c and overlay it with the plot of f. Calculate the norm error and mean norm error of the interpo- lation and compare with your results in part c of problem 2. an interesting technique designed specifically for non-linear equations in one spatial dimension. We begin with the formal definition. Definition 3.5.1. Suppose that f is a differentiable function on (a, b) and take a