SOLUTION: The curve y=ax^3+2x^2+a^2x+b has a minimum point at (-1,0). Find a and b.

Question 1044048: The curve y=ax^3+2x^2+a^2x+b has a minimum point at (-1,0). Find a and b.
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
----Must be for .

Let x=-1;
, from the derivative being 0 when x is -1;

ALSO from the original equation,

so the problem gives the system of equations,

Solve this system (first, for "a", and then for b).

-
First equation of the system is factorable.

and the description gave, ",... has a minimum point at (-1,0)".

Either the equation becomes or . Do you believe that the second-derivative might give further information about x at -1 being minimum or maximum?
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