Originally Posted by

**avisccs** I want to be clear about the concept of second derivative.

I would be able to tell whether a critical point is maximum or minimum from a second derivative. If second derivative is negative, the critical point is a maximum. If the second derivative is positive, the critical point is a minimum.

What if the sign of the second derivative depends on the value of x.

For example, I already know $\displaystyle x \in [0,\infty] $, and my second derivative is $\displaystyle x - 3$. So the second derivative is negative when x<3, positive when x>3 and 0 when x = 3. What does it tell me about the critical point? Please note I don't know what the critical point(s) are yet. Does this second derivative indicate more than one critical points?