SOLUTION: Find the values of a and b so that the function f(x)=(1/3)x^3 + ax^2 +bx will have a local extrema at (3,1).

Question 1106177: Find the values of a and b so that the function f(x)=(1/3)x^3 + ax^2 +bx will have a local extrema at (3,1).
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

We know that...

(a) f(3) = 1:

(1)

and

(b) f'(3) = 0:
f'(x) = x^2+2ax+b

(2)

Solve the pair of equations (1) and (2).

The numbers turn out to be ugly fractions, so solve for both a and b using elimination.

solve for a (eliminate b):

solve for b (eliminate a):

The required function is

The graph shows a relative minimum at (3,1):

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