Differentiating, we obtain:
       f'(x)=alltermsfpr=factoredfpr
Factor f'(x), if possible.

The factorization is given by f'(x)=3*p(x+2*a)(x-2*b).

Using this factorization,
      figure out where the derivative f'(x) is positive and negative.
Notice that f'(x) is positive when x is a large positive number.
Work along the number line from right to left.

The derivative f'(x) is        positive on xmin < x,
                                             negative on xmax < x < xmin and
                                             positive on x < xmax.

Then the function f(x) is    increasing on xmin < x,
                                             decreasing on xmax < x < xmin and
                                             increasing on x < xmax.

Now enter xmax and xmin into the Answer boxes, to indicate that xmax < x < xmin is the largest (bounded) open interval of decrease.

NOTE: The next two hints show: the graph of f, followed by the graph of f'.
Note that the graph of f runs downhill between x = xmax and x = xmin.
Note that the graph of f' is below the x-axis between x = xmax and x = xmin.

initAutoscaledGraph( [ xrange , yrange ], {} ); style({ stroke: "#6495ED", strokeWidth: 3 }, function() { plot( function( x ) { return p*x*x*x+q*x*x+r*x+s; }, [-10,10] ); });

initAutoscaledGraph( [ [ -10, 10] , [ -500, 500] ], {} ); style({ stroke: "#6495ED", strokeWidth: 3 }, function() { plot( function( x ) { return 3*p*x*x+2*q*x+r; }, [-10,10] ); });