# find a and b given point of inflection and local min.

• Jan 16th 2009, 07:17 AM
h4hv4hd4si4n
find a and b given point of inflection and local min.
The function f(x) = x^3 + ax˛ + bx has a local minimum at x=3 and a point of inflection at x = -1. Find the values of a and b.

I don't even know where to begin on this problem; any help is appreciated.
• Jan 16th 2009, 07:32 AM
earboth
Quote:

Originally Posted by h4hv4hd4si4n
The function f(x) = x^3 + ax˛ + bx has a local minimum at x=3 and a point of inflection at x = -1. Find the values of a and b.

I don't even know where to begin on this problem; any help is appreciated.

The condition for an extremal point is f'(x) = 0 and the condition for a point of inflection is f''(x) = 0

\$\displaystyle f(x) = x^3+ax^2+bx\$

\$\displaystyle f'(x)= 3x^2+2ax+b\$

\$\displaystyle f''(x)=6x+2a\$

Plug in the values you know:

\$\displaystyle f'(3) = 0 = 27+6a+b\$

\$\displaystyle f''(-1)=0= -6+2a\$

Solve this system of simultaneous equations for a and b.
• Jan 16th 2009, 07:40 AM
h4hv4hd4si4n
I got a = 3 and b = -45

is that correct?
• Jan 16th 2009, 07:44 AM
earboth
Quote:

Originally Posted by h4hv4hd4si4n
I got a = 3 and b = -45

is that correct?

I've got the same result. (Clapping)
• Jan 16th 2009, 07:46 AM
h4hv4hd4si4n
thanks for your help