# The rate of change definition is very simple

Practically, the quotient of the division of the change in the output value and the change in the input value of a function is mainly known as the **rate of change. **Basically, we **define rate of change** as a number that shows the relationship between the two variables in equation. In most of the situations, the rate of change coincide with the coefficient x of an equation.

## Some important rate of change problems

Now that you know **what is rate of change**, in order you can make a better idea what is this all about, we will provide you some **rate of change problems**. Basically, you will have to find a series of **rates of change**. But first we will go with some of the important equations and then proceed with **rate of change word problems**.

The **relative rate of change **of a function f(x) is given by the relation f'(x)/f(x) , where f'(x) is the first derivative of the function. The displacement in position is also called the rate of change in position. Considering that a particle's initial position is A, and then after a time t it arrives in the second point (B), then rate of change is equal to (particle at B – particle at A)/time. The rate of change in velocity is given by (Final velocity – Initial velocity)/time. Similarly rate of change in acceleration is (final acc – initial acc)/time. The maximum rate of change can only be obtained when vector v is into the same direction of the gradient f(x,y). Therefore, the maximum rate of change represent the magnitude of the gradient (x,y).

## Some important rate of change examples

We have seen what is rate of change in math. Now we will provide you with some rate of change examples.

Problem 1: Given the following points A(6,8) and B(0,-4), find their rate of change. Use the general **calculus rate of change** model.

We have: x_{1}=6, x_{2}=0 and y_{1}=8, y_{2}=-4. From the **definition of rate of change,** (y_{2} – y_{1})/(x_{2} - x_{1)} = (-4 - 8)/(0-6) = 2. The change rate is 2.

Problem 2: Given the following algebraic equation y = 4x + 9, calculate its rate of change:

Rate of change = dy/dx. Therefore, Differentiating with respect to x, dy/dx = 4 which implies that the rate of change of y is 4.

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