Chapter 7, Problem 38P

To determine

(a)

To write:

A user-defined function that calculates the derivative of a math function by using the two-point central difference formula such that $\text{dfdx}=\text{FoPtder(Fun,x0)}$ is used as a function name and arguments; a program in a script file that uses the $\text{FoPtder}$ function to determine the derivative of $f\left(x\right)=x^3{e}^{2x}$ at $x_0=0.6$. (Compare the answer obtained from $\text{FoPtder}$ with the analytical solution.)

To determine

(b)

To write:

A user-defined function that calculates the derivative of a math function by using the two-point central difference formula, such that $\text{dfdx}=\text{FoPtder(Fun,x0)}$ is used as a function name and arguments; a program in a script file that uses the $\text{FoPtder}$ function to determine the derivative of $f\left(x\right)=\frac{3^x}{x^2}$ at $x_0=2.5$. (Compare the answer obtained from $\text{FoPtder}$ with the analytical solution.)