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 , and my second derivative is . 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?
My function is super-complex with 2 variables, I can't do it using algebra, but I can optimise it using Optim function in R. I'm trying to understand the result, whether it is a local or global maxima. I tried plotting, but still not sure. One can never plot from - infinity to infinity. So I now try to find any indication of problems with my result, starting with one variable and will go onto 2 variables. I know the derivative for 2 variable functions is different from single variable function.
Perhaps you should post your function...