function [result] = test_function1 (x, n)
% test_function1(x,n) calculates the n'th derivative of a test function 
%   for a vector of points x.
%
%   Input arguments:
%     x = where to evaluate the function or derivative (vector)
%     n = 0 to return the function value at x, 1 to return the first
%          derivative, 2 to return the 2nd derivative
%   Output arguments:
%     result = value of the function or derivative 

%
% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
%
% Revision history:
%   24-Mar-2005 -- original version for Physics 263
%   07-Apr-2005 -- switched to another function (bad first choice)
%
% Notes:
%   * This is a MATLAB "function" file like circle_area.m.
%   * To change the test function, you must insert the correct expression
%      for the function, first derivative, and second derivative by
%      hand below.
%   * In order to handle vectors x, we use ".*" in the function 
%      definition. 
%   * Possible upgrades:
%       * Can we generate the derivatives symbolically using "diff"?
%

% calculate the test function or derivative(s) according to the value of n 
switch n

    case 0
      % calculate the function (the ";" at the end suppresses the output)
      result = exp(-x);

    case 1
      % calculate the first derivative
      result = -exp(-x);
    
    case 2
      % calculate the second derivative
      result = exp(-x);
      
    otherwise
      % notify the user of an error
      disp('illegal choice for n')
    
end      % this ends the "switch"