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 = 27-6a+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 27-6a+b in terms of a, I get a= 27+b/6.

But what do I plug in for b?

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