Differentiable Function

Definition

A differentiable function is a type of function that has derivatives at every point within its domain. This means that the slope or rate of change can be determined at any point on the graph.

Analogy

Imagine driving on a smooth road with no bumps or potholes. A differentiable function is like this road because it allows us to smoothly calculate the slope or rate of change at any point without encountering any sudden changes or disruptions.

Related terms

Derivative: The derivative measures how much a function changes as its input changes. It represents the instantaneous rate of change or slope at any given point on the graph.

Tangent Line: A line that touches and "hugs" the curve of a differentiable function at only one point, representing the instantaneous rate of change (slope) at that specific point.

Critical Point: A critical point occurs when either the derivative is zero or undefined. These points are important for determining maximums, minimums, and inflection points on graphs.