In calculus, a branch of mathematics, the second derivative test determines whether a given stationary point of a function (where its first derivative is zero) is a maximum, a minimum, or neither.
The first derivative test relates the condition of being a maximum or a minimum to a condition on the positivity or negativity of the first derivative. The second derivative test works by rephrasing the condition on the first derivative in terms of the second derivative. Suppose that f is twice differentiable in a neighbourhood of a stationary point x. The test says:
If there exists a positive number r such that f'' is continuous between x-r and x+r, and if f''(x) is positive, then f has a minimum at x.
If there exists a positive number r such that f'' is continuous between x-r and x+r, and if f''(x) is negative, then f has a maximum at x.
If f'' is not continuous between x-r and x+r for any r, or if for some r, f'' is continuous between x-r and x+r but f''(x) is zero, then the test fails.
If the secondderivative is positive at a critical point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
Acceleration is the derivative (with respect to time) of an object's velocity, that is, the secondderivative (with respect to time) of an object's position.
Jerk is the derivative (with respect to time) of an object's acceleration, that is, the third derivative (with respect to time) of an object's position, and secondderivative (with respect to time) of an object's velocity.
The TESTSECOnd command, tests the secondderivative of the energy by finite difference of the forces.
TEST NOCO WRITE command has to be performed on a single CPU and writes all the necessary data from memory to a file specified by UNIT keyword.
TEST NOCO READ has the same parameters as WRITE, but the complete information is stored to the memory from the file for the number of steps specified with the STEP keyword.
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