Rate of change refers to the speed at which a particular variable changes over a given period of time. We can define this in several ways, such as “A rate that tells how one quantity changes in relation to another quantity is called the rate of change”. The other way of defining it is using variables like “If x is an independent variable and y is the dependent variable, then the rate of change of these can be the ratio of change in the variable y to the change in variable x”.
We know that the rate of change is one of the major applications of derivatives in calculus. For example, for any function, the rate of change is obtained by differentiating the given function. Sometimes this differentiation leads to partial differential equations when the function involves more than one independent variable. Rates of change can be negative or positive or zero. This corresponds to a decrease or increase in the value of y between the two given data points. If a quantity does not undergo any change over the given time, then it is called a zero rate of change.
Differentiation is an essential tool for finding the minimum or maximum value of a given function under certain conditions. This could be understood in a better way through the above-mentioned application. In some cases, the function may not be discrete, that means, it can be a continuous function. In such cases, differentiating the function may not give an accurate result. There are other calculus formulas that exist to perform the required operation on these types of functions.
The solution of different types of responses and differential equations are obtained algebraically with the help of Laplace transform, which results in a simple and yet significant solution to the convolution integral. For a given function, finding the Laplace transform is not difficult, if we’ve got a table of transforms to perform this. Also, we knew that this could be a more lengthy and challenging process than taking transforms. In such cases, finding the inverse laplace transform of the function is an ideal decision.
However, all these will come under integration in calculus, the other important branch along with differentiation. Though there is no such relation between the rate of change and area enclosed or covered by the curves or lines, the functions formed with these situations lead to perform some similar mathematical operations to get the desired results. Besides, the rate of change in quantities are not only restricted with respect to time, speed -distance, but also involves the change of prices of commodities with respect to other related factors in the business world.