Part 3/6:
If ( f''(x) > 0 ), the function is concave upwards, indicating that the first derivative is increasing.
If ( f''(x) < 0 ), the function is concave downwards, meaning that the first derivative is decreasing.
This relationship highlights the integral connection between the concavity of the graph and its first and second derivatives.
Inflection Points: Defining Moments of Change
An inflection point occurs where a graph changes its concavity. Such points signify transitions, for instance, shifting from concave upwards to concave downwards or vice versa. Identifying an inflection point involves recognizing where the second derivative is zero or undefined, leading to a change in concavity.