Consider the general cubic function y = ax3 + bx2 + cx + d. Let the maximum point be Point A, and the minimum point be Point B. Proof that the inflection point lies on the line AB. Argument should contain enough calculation evidence and any limitations on the constants a, b, c and/or d.

Question

Consider the general cubic function y = ax3 + bx2 + cx + d. Let the maximum point be Point A, and the minimum point be Point B.  Proof that the inflection point lies on the line AB. Argument should contain enough calculation evidence and any limitations on the constants a, b, c and/or d.

freckles · Answer

I would be probably start of drawing of what they want me to prove....
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I didn't extend the graph too far since we are looking at the locals here.