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 –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.