f''(0)
The notation "f''(0)" represents the second derivative of a function f evaluated at the point x = 0. The second derivative measures how the rate of change of the function's slope is itself changing. In simpler terms, it tells us about the curvature of the graph of f at that specific point.
When f''(0) is positive, it indicates that the graph is curving upwards at x = 0, suggesting a local minimum. Conversely, if f''(0) is negative, the graph is curving downwards, indicating a local maximum. If f''(0) equals zero, the behavior of the graph at that point may require further analysis.