Second Derivative

Definition

The second derivative of a function represents the rate at which the slope of the original function is changing. It measures how the rate of change of the first derivative changes.

Related terms

Concavity:

Concavity refers to whether a graph curves upward or downward. A graph is concave up when its second derivative is positive, meaning it's bending upwards like a smiley face.

Inflection Point:

An inflection point occurs where the concavity of a graph changes. It happens when the second derivative changes sign, indicating that the curve transitions from being concave up to concave down or vice versa.

Critical Point:

A critical point is where either the first or second derivative equals zero or does not exist. These points can be local maxima, minima, or points of inflection depending on their behavior around them.