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Differential Equations Terms

Get down with the lingo

Differential Equation

An equation that relates the values of the function with the derivatives of the function.

Order Of A Differential Equation

The highest derivative that appears in the differential equation.

Slope Field

A graphical representation of a differential equation by plotting the slopes.

Equilibrium Solution

A solution to a differential equation whose derivative is zero everywhere.

Stable Equilibrium Solution

An instance when a solution starts close to the stable equilibrium solution and gets closer to the stable equilibrium solution.

Unstable Equilibrium Solution

An instance when a solution starts close to the unstable equilibrium solution and gets far away from the unstable equilibrium solution.


This describes whether the function is curving up, down or not curving at all.

Critical Point

The derivative of the function at the critical point is 0.

Inflection Point

The point (x-value) where the function changes concavity.

Implicit Differentiation

Differentiation of an equation in which the dependent variable doesn't have a side of the equation all to itself.

Derivative Of A Function

The derivative of f (x) measures how f (x) changes at a point x.

Local Extreme Point

The maximum and minimum point when the domain is restricted to a small neighborhood of x –values.

Global Extreme Point

The maximum and/or minimum points in the entire domain of the function.

Secant Line

Line joining two points on the graph of a function.

Tangent Line

A line that touches the graph of a function f (x) at a point.


If the limit exists, the function f (x) is differentiable at x = a.

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