You are to write a program in Matlab to evaluate the forward finite difference, backward finite difference, and central finite difference approximation of the first derivative of the following function:

$f(x)=0\mathrm{.}1-2\mathrm{.}25xsinh(1\mathrm{.}02x)$

at the location $x_0=0\mathrm{.}245$ using a step size of $x=0\mathrm{.}1,0\mathrm{.}01,0\mathrm{.}001$dots${10}^{-20}.$ Evaluate the exact derivative and compute the error for each of the three finite difference methods.

Generate a table of results for the error for each finite difference at each value of $x.$

Generate a plot containing the log of the error for each method vs the log of $x.$

Repeat this in single precision.

What is machine epsilon in the default Matlab real variable precision.

What is machine epsilon in the Matlab real variable single precision.

Instructions: your project files should have a comment that has

Your name.

Due date of the project.

Name of the project.

Submit your Matlab project files along with output generated for questions $1-3$ on