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: x1=6, x2=0 and y1=8, y2=-4. From the definition of rate of change, (y2 – y1)/(x2 - x1) = (-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.
San Francisco, USA
"If you're at school or you just deal with mathematics, you need to use Studygeek.org. This thing is really helpful."
"I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. "
" I'm a geek, and I love this website. It really helped me during my math classes. Check it out) "
"I use Studygeek.org a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"