Posted by Sarah on Wednesday, March 10, 2010 at 7:20pm.
Find constants a,b and c such that the graph of f(x)=x^3+ax^2+bx+c will increase to the point (3,18), decrease to the point (1,14) and then continue increasing.

Calculus  Damon, Wednesday, March 10, 2010 at 7:27pm
Find constants a,b and c such that the graph of f(x)=x^3+ax^2+bx+c will increase to the point (3,18), decrease to the point (1,14) and then continue increasing.
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The derivative is zero at x = 3 and x = 1
f' = 3 x^2 + 2ax + b
0 = 3(9) +2a(3) +b = 276a+b
and
0 = 3(1) +2a(1) +b = 3 +2a+b
so solve those two equations for a and b
then use the value of y = 1 at x = 1 to get c 
Calculus  Sarah, Wednesday, March 10, 2010 at 7:45pm
Thank you Damon, but I still do not understand.
How do I solve for a, if I rearrange 276a+b in terms of a, I get a= 27+b/6.
But what do I plug in for b?