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

Fundamental theorem of integral facts formulasproperties, Fundamental Theor...

Fundamental Theorem of Calculus, Part I If f(x) is continuous on [a,b] so, g(x) = a ∫ x f(t) dt is continuous on [a,b] and this is differentiable on (a, b) and as,

Tutor, how can i apply as tutor

how can i apply as tutor

Calculate how much ribbon is needed to wrap the box, Ribbon is wrapped arou...

Ribbon is wrapped around a rectangular box that is 10 by 8 by 4 in. Using the example provided, calculate how much ribbon is needed to wrap the box. consider the amount of ribbon d

Application of statistics-quality control, Quality Control Normally th...

Quality Control Normally there is a quality control departments in every industry which is charged along with the responsibility of ensuring about the products made do meet th

Describe segments, Describe Segments, Rays, Angles, and Triangles We now...

Describe Segments, Rays, Angles, and Triangles We now define some more basic geometric figures. 1. Segments Definition A segment is the set of two given points and all the

HELP, WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357

WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357

Shares and dividends, suresh invested rs.1080 in shares of face value rs.50...

suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d

Assignment Help, I would like to work on Assignment help in Mathematics

I would like to work on Assignment help in Mathematics

Triangle and its properties, in a triangle angle a is 70 and angle b is 50 ...

in a triangle angle a is 70 and angle b is 50 what is angle c.

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