Use a Taylor series expansion to derive a centered finite- difference approximation to the third derivative that is second- order accurate. To do this, you will have to use four different expansions for the points x_i-2, x_i-1, x_i+1, and x_i+2. In each case, the expansion will be around the point x_i. The interval ∆x will be used in each case of i - 1 and i + 1, and 2∆x will be used in each case of i - 2 and i + 2. The four equations must then be combined in a way to eliminate the first and second derivatives. Carry enough terms along in each expansion to evaluate the first term that will be truncated to determine the order of the approximation.