HW16: Function numder

     One area where function pointers are used extensively is in
numerical computing.  Many numerical methods such as minimization
and optimization, require the derivative of the mathematical
function which is being analyzed.  Rather than writing a separate
derivative function for each mathematical function (and in some
cases the derivative can not be written in closed form), a
general purpose numerical derivative function can be written to
work with any differentiable function.  Consider the following
algorithm for a numerical derivative:

        df(x)/dx ~= (f(x+h) - f(x-h))/2h

(The ~= means approximately equal, I have omitted an error term
from the equation.)  The error in this approximation is proportional
to h*h.  Thus, a small value of h will give a better numerical
derivative.

     Based upon this algorithm, write a function, numder(), which
accepts three parameters.  The first is a pointer to a function
that accepts a double argument and returns a double value.  The
second parameter is the value of x (type double) where the numerical
derivative is to be evaluated.  The third parameter is a double
variable that contains the value of h.  Thus the user of the
function numder can specify the precision with which the numerical
derivative is calculated.  The function returns the numerical
derivative (also a double variable).

     You may want to define a function pointer type.  If you do,
make sure that you include the typedef in the numder.h file.
Otherwise, numder.h would contain the function prototype.

SUBMITTING YOUR HOMEWORK:

        Use the toteach command to submit numder.c & numder.h