When concavities are equal to a number or a constant, what does it mean?
For example, f''(x) = 3, and f''(x) = 0 when x = 2. What does 2 = 3 mean? And when it is f''(2) = 0 it is a point of inflection correct?
The second derivative being zero does not imply that there is a point of inflection. If you know you have a point of inflection, then the second derivative is zero. So the implication only works one way. My favorite mnemonic device for remembering the second derivative test is the following:
I can answer you better if you refine your questions.