Thread: Local minimum and inflection

Let f(x) = x^3 + ax^2. What is the value of a if
(a) f has a local minimum at x = 4?
(b) f has a point of inflection at x = 6?

How do I find a given the local minimum and point of inflection?
Thanks.

Originally Posted by Såxon

Let f(x) = x^3 + ax^2. What is the value of a if
(a) f has a local minimum at x = 4?
(b) f has a point of inflection at x = 6?

How do I find a given the local minimum and point of inflection?
Thanks.

To find a local minimum you should take the first derivative.

To find the point of inflection you should take the second derivative.

Ah, i see, thanks.