This Java applet computes the value and the gradient of a function at a
The function f(x,y) can be chosen freely, using the standard
arithmetic operations +, -, *, /,
^ (integer power) and the standard functions sin,
cos, exp and sqrt.
The point (x,y) at which the function is evaluated can also be chosen
by the user. Numerical constants are either floating point constants like
3.141, or intervals formed by such constants, for example [3.141, 3.142].
Intervals may also be used in the definition of the function.
- Evaluate the default function for different values of (x,y).
In particular, choose intervals of different width, including width zero.
- Change the function to f(x,y):=x-x. Evaluate it at x=[1,2].
Surprised? This shows that two identical functions (f=x-x and f=0
in our case), defined by different expressions, may evaluate to drastically
- Now change the function to f(x,y):=x*y, and evaluate it for
different values of (x, y). Can you always predict the results?
- Finally, define f(x,y):=x/y, and evaluate it at (x, y)=(1,
Last modified by Wolfgang Kühn on
Sunday, 10 October 1999