Consideration of this function reveals that for large positive values of z the cubic term dominates and the function value is a large negative number. For large negative values of z, the cubic term again dominates and the function has a large positive value. There is a local minimum and a local maximum nearer to the origin.

We select the Optimize… option from the menu and ask the program to find the minimum of H starting at 0 for the variable z. The program discovers that at z = 0, the gradient is 10 and the normalized gradient is 1. Moving in the direction of the greatest decrease, the line search finds the minimum at z = -9.37783. For a single dimension, the Hessian is simply the second derivative of the function at the stationary point. Since it is positive, the analysis concludes that this is indeed a local minimum

In a similar manner we find the local maximum of H by moving in the positive direction.

It should be noted that the results of the direct search depend strongly on the starting point.