Final answer:
The number 0 in second partial derivatives indicates an inflection point, which by itself is neither positive nor negative. It is a point where the concavity of a function or surface changes, and its stability depends on the evaluation of the second partial derivatives around this point.
Step-by-step explanation:
In the context of second partial derivatives, the number 0 is neither considered positive nor negative. The second partials refer to the concavity of a surface or a curve in a certain direction, and when a second partial derivative is equal to 0, it suggests a point of inflection where the concavity changes. This inflection point may suggest a potential change from a relative maximum to a relative minimum or vice versa, but it is not indicative of stability or unstableness by itself.
When evaluating whether a function reaches a relative maximum or minimum, both signs of the second partial derivatives are investigated. If the second derivative test reveals a positive value, it indicates a relative minimum and a stable equilibrium. Conversely, a negative value suggests a relative maximum and an unstable equilibrium. It is important to evaluate the signs around the inflection points where the second partial derivatives are 0 to determine the nature of these points.