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

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

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

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

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.

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