Chapter 7, Problem 39P

The first derivative $\frac{df(x)}{dx}$ a function f(x) at a point x = x₀can he approximated with the four-point central difference formula:

$\frac{df}{dx}=\frac{f(x_0-2h)-8f(x_0+h)+8f(x_0+h)-f(x_0+2h)}{12h}$

where h is a small number relative to x₀. Write a user-defined function (see Section 7.9) that calculates the derivative of a math function f(x) by using the four-point central difference formula. For the user-defined function name, use dfdx=FoPtder (Fun, x0), were Fun is a name for the function that is passed into FoPtder, and x₀is the point where the derivative is calculated. Use h=x₀/100 in the four-point central difference formula. Use the user-defined function FoPtder to calculate the following:

(a) The derivative of f(x) = x³e^2x at x₀= 0.6.

(b) The derivative of $f(x)=\frac{3^x}{x^2}$at x₀=2.5.

In both cases compare the answer obtained from FoPtder with the analytical solution (use format long).