Table of Contents
How do you classify stationary points?
A stationary point x is classified based on whether the second derivative is positive, negative, or zero. If the test is inconclusive, we must use some other method to determine the nature of the stationary point (such as the first derivative test).
What is the second derivative rule?
If the second derivative is positive over an interval, indicating that the change of the slope of the tangent line is increasing, the graph is concave up over that interval. CONCAVITY TEST: If f ”(x) < 0 over an interval, then the graph of f is concave upward over this interval.
How do you know if a stationary point is maximum or minimum?
The second derivative test is used to determine whether a stationary point is a local maximum or minimum. A stationary point x is classified based on whether the second derivative is positive, negative, or zero….Second Derivative Test.
| d2ydx2 | Stationary point at x |
|---|---|
| >0 | Local minimum |
| <0 | Local maximum |
| =0 | Test is inconclusive |
What is second order derivative?
The second derivative, or second order derivative, is the derivative of the derivative of a function.
What is the second derivative test?
The second derivative test is specifically used only to determine whether a critical point where the derivative is zero is a point of local maximum or local minimum. Note in particular that: For the other type of critical point, namely that where is undefined, the second derivative test cannot be used.
What does dy dx represent?
dy/dx represents the instantaneous rate of change of variable y with respect to x,where dy is an incremental change in y for an incremental change in x.
What does the second derivative show?
The second derivative is like the movie Inception. The first derivative tells us whether or not the function is increasing or decreasing. The second derivative shows us whether or not the first derivative is increasing or decreasing.