Final answer:
The purpose of computing right-hand and left-hand derivatives at a point is to examine the function's instantaneous rate of change at that point, reflecting the slope of the tangent there.
Step-by-step explanation:
When computing the right-hand and left-hand derivatives as limits for a function at point P, the primary purpose is to examine the function's instantaneous rate of change at P. This calculation of derivatives as limits is a fundamental concept in Calculus, which is the mathematics of change. It involves the study of limits, derivatives, integrals, and infinite series. By determining the derivatives from the right and left, we essentially investigate the slope of the tangent line to the function at point P, which tells us how the function is changing at that specific point.
For physical quantities, the dimension of the derivative of one quantity with respect to another is the ratio of the dimensions of these quantities. For example, if v represents velocity and t represents time, then the dimension of the derivative dv/dt would be the ratio of the dimension of v over that of t, which signifies the rate of change of velocity with respect to time or acceleration.