Final answer:
The derivative of an equation represents the instantaneous rate of change at a specific point in time. By finding the derivative of a function and analyzing its sign changes, you can determine when the instantaneous velocity is greatest, zero, or negative.
Step-by-step explanation:
In physics, the derivative of an equation represents the instantaneous rate of change at a specific point in time. The derivative of a function can be used to determine when the instantaneous velocity is greatest, when it is zero, and when it is negative.
To determine these values, you would need to find the derivative of the given equation and set it equal to zero to find the critical points. The points where the derivative is positive represent when the velocity is positive, and the points where the derivative is negative represent when the velocity is negative.
By analyzing the sign changes of the derivative, you can determine the times at which the instantaneous velocity is greatest, zero, or negative.