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20 13 Anhui college entrance examination mathematics and physics volume multiple-choice questions 10 detailed answers.
Solution: f ′ (x) = 3x 2+2ax+b, x 1, where x2 is the two roots of the equation 3x 2+2ax+b = 0,

If 3(f(x))2+2af(x)+b=0, then there are two f(x) that make the equation hold.

X 1=f(x 1), assuming that X2 > x 1 and x 1=f(x 1), then x1is the maximum point.

The following schematic images:

At this point, there are three intersections,

On the other hand, if x2 < X 1, x 1=f(x 1), then X 1 is the minimum point.

So choose a.