Given a general cubic function y = ax^3 + bx^2 + cx + d prove the...

Given a general cubic function y = ax^3 + bx^2 + cx + d prove the following,

a) That a cubic must change at a quadratic rate.

I believe this to be the derivative of the general cubic function, yielding dy/dx = 3ax^2 + 3bx + c

b) That there are only 6 basic forms (shapes) for a cubic.

This question is where I get lost. Please help, Thanks!

Expert Solution

To show that a cubic function must change at a quadratic rate and there are only 6 basic forms of a cubic function.

milcah answered 2 years ago

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Given a general cubic function y = ax^3 + bx^2 + cx + d prove the...

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