Rates of change or instantaneous rate of change, Mathematics

Assignment Help:

Rates of Change or instantaneous rate of change ; Now we need to look at is the rate of change problem.  It will turn out to be one of the most significant concepts .

We will consider a function, f(x), which represents some quantity which varies as x varies.  For example, maybe f(x) represents the amount of water into a holding tank after x minutes. Or possibly f(x) is the distance traveled through a car after x hours.  In both of these example we utilized x to represent time.  Certainly x doesn't need to represent time, however it makes for examples that are easy to visualize.

What we desire to do here is determine just how fast f(x) is verifying at some point, say x = a.  It is called the instantaneous rate of change or sometimes just rate of change of f(x) at x = a .

As along the tangent line problem all that we're going to be capable to do at this point is to find out the rate of change.  Hence let's continue with the instance above and think of f(x) as something i.e. changing in time and x being the time measurement. Again x doesn't need to represent time but it will make the clarification a little easier. Whereas we can't calculate the instantaneous rate of change at this point we can find the average rate of change.

To calculate the average rate of change of f(x) at x = a all we have to do is to select another point, say x, and then the average rate of change will be,

                A.R.C. = change in f ( x ) /change in x

                              = f ( x ) - f ( a ) /x - a

Then to estimate the instantaneous rate of change at x = a all we have to do is to decide values of x getting closer & closer to x = a (don't forget to decide them on both sides of x = a ) and calculate values of A.R.C. Then we can estimate the instantaneous rate of change from that.


Related Discussions:- Rates of change or instantaneous rate of change

Example of linear equations, Example of Linear Equations: Solve the eq...

Example of Linear Equations: Solve the equation 2x + 9 = 3(x + 4). Solution: Step 1. Using Axiom 2, subtract 3x and 9 from both sides of the equation. 2x + 9 = 3(

Define a*b for given matrix, Define A*B where:                A =  | 3 -...

Define A*B where:                A =  | 3 -3  6 |          B = |  6   1 |                          | 0  4  2 |              |  0  -5 |

Extreme value theorem, Extreme Value Theorem : Assume that f ( x ) is cont...

Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and

Fractions, how to add a fraction with an uncommon denomoninator

how to add a fraction with an uncommon denomoninator

Exponent, base also called what

base also called what

Geometry help, One of two complementary angles is 80& of the other. What is...

One of two complementary angles is 80& of the other. What is the degree measure of the smaller angle?

What is dividing fractions, What is Dividing Fractions? If you want to ...

What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication

Calculate the linear equation, Calculate the linear equation: Example...

Calculate the linear equation: Example: Solve the equation 4x + 3 = 19 by transposing. Solution: Step 1. Transpose the 3 from the left-hand to the right-hand si

People fit, How many people ca fi in a small cars without seats?

How many people ca fi in a small cars without seats?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd