The contour plot of Rosenbrock's function for **n=2** is shown
in Figure 3. In general, contour maps show surfaces in
the -dimensional space defined by
where is a constant.
For **n=2**, * plane* curves correspond to various values of
. We see from the figure that
the minimum point (dark circle)
is at , where .
The gradient components of this function are given by

and the Hessian is the block diagonal matrix with entries

(These formulas are given in a form most efficient for programming.)
For **n=2**, the two eigenvalues of the Hessian at the minimum
are and , and thus the
condition number . The function contours, whose axes lengths
are proportional to the inverse of the eigenvalues,
are thus quite elongated near the minimum (see Figure 3).