First Derivative

Definition

The first derivative represents the rate at which a function is changing at any given point. It measures the slope of the tangent line to the graph of a function at that point.

Related terms

Second Derivative:

The second derivative represents the rate at which the first derivative is changing. It helps determine whether a function is concave up or concave down.

Critical Points:

Critical points are locations where either the first derivative equals zero or does not exist. They can indicate maximums, minimums, or inflection points on a graph.

Rate of Change:

Rate of change refers to how quickly one quantity changes with respect to another quantity. In calculus, it often involves finding derivatives to measure this rate accurately.