Thread: find a and b given point of inflection and local min.

The function f(x) = x^3 + ax² + 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.

Originally Posted by h4hv4hd4si4n

The function f(x) = x^3 + ax² + 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







Plug in the values you know:





Solve this system of simultaneous equations for a and b.

I got a = 3 and b = -45

is that correct?

Originally Posted by h4hv4hd4si4n

I got a = 3 and b = -45

is that correct?

I've got the same result.

thanks for your help