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.
A graphical representation of a differential equation by plotting the slopes.
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.
The derivative of the function at the critical point is 0.
The point (x
-value) where the function changes concavity.
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
) measures how f
) changes at a point x
Local Extreme Point
The maximum and minimum point when the domain is restricted to a small neighborhood of x
Global Extreme Point
The maximum and/or minimum points in the entire domain of the function.
Line joining two points on the graph of a function.
A line that touches the graph of a function f
) at a point.
If the limit
exists, the function f
) is differentiable at x