Find the stationary points of the function M

(a,

b) = 2a 3 +

6ab2−3b 3−150a, and identify the extrema by drawing a graph of the surface. (Hint: this is a bit tricky. You will probably need to fiddle with the vertical scale of the graph to make all the humps appear clearly. Then you may need to rotate it around a bit to see where all the stationary points are.)

Extrema don’t have to occur at isolated points, but can occur along lines or circles. In this example, the maxima and minima occur in circles.