To understand means the ability to create external world model and predict its reactions. In this case it means that the machine has to create:

1. A model for determining function’s maximum, minimum or bend point where derivative dy/dx = 0. In this case to solve the equation dy/dx= -4x+a=0, i.e., to find the xo coordinate xo=a/4.

2. A model for determining wether the found point is maximum, minimum or bend point: when the second derivative is positive, the function has its minimum, when it is negative, the function has maximum, and when it = 0, the function has a bend point. In this case to calculate the second derivative d2y/dx = -4. The second derivative is negative, the function has a minimum at xo=a/4.

3. A model for calculating the minimum point y coordinate: yo= f(xo) = -2×2+axo+b= a2/8 +b.

]]>The parabola is given by y = -2xsquared + ax +b.

Set dy/dx = -4x + a =0. Solve for x = a/4. Replace x in equation and solve for b when y = 0 = -2asquared/16 + asquared/4 + b = asquared/8 + b.

The vertex of this parabola is a function of (a,b) and = (a/4, asquared/8 +b). ]]>