Objective Using MatLab with user entered anonymous functions.

Project The instantaneous rate of a change of a function is an important application in engineering.

In its purest sense it is the derivative of a function, but in programming it is necessary to

implement it as an approximation.

Write a program the prompts the user to enter a function as a string of text. This func$-$

tion should be made into an anonymous function. This is all to be done in the function

get$\_$function.

It will then ask for a value of an input point at which your program will estimate the derivative

of the entered function. The program should also plot a graph of the function on an interval

surrounding the point, as well as drawing the tangent line on the graph at the point.

The estimate of the derivative for a function $f(x)$ is

$f^{\text{'}}(x)=\underset{x_1{x}_0}{lim}\frac{f(x_1)-f(x_0)}{x_1-x_0}$

$=\underset{x0}{lim}\frac{f(x_0+x)-f(x_0)}{x}$

This is not the code for the program. You will convert it to the appropriate MatLab code. You

DO NOT take a limit$.$ Instead hard code a deltaX with an appropriately small value in the

derivative function and use it$.$

The template includes a function, plot$\_$function$\_$tangent that will plot the function that

the user enters, and the tangent line at the point that you select.

The program must be written using top$-$down design.

Remember that every program that you submit must include an introduction consisting of

your name, the date, and a description of the program as both comments at the begin$-$

ning of the program and as text that is printed when you first run the program $-$ the printed

component should be your print$\_$header function..