# Differential Equations

### Terms

### 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.### Concavity

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*â€“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.

### Differentiability

If the limit exists, the function*f*(

*x*) is differentiable at

*x*=

*a*.

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