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 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.