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

Percent problems.., I have a graph, i need to determine the many hours per ...

I have a graph, i need to determine the many hours per day becky spends on math activity if she does it 25% of her day.

Find the quotient and remainder, Question: Find the quotient and remain...

Question: Find the quotient and remainder when f(x) = x 5 - x 4 - 4x 3 + 2x + 3 is divided by g(x) = x-2. Make sure the quotient and remainder are clearly identified.

Stat, defination of uper boundarie .

defination of uper boundarie .

Course work2 , (b) The arity of an operator in propositional logic is the n...

(b) The arity of an operator in propositional logic is the number of propositional variables that it acts on – for example, binary operations (e.g, AND, OR, XOR…) act on two propo

Objectives of addition and subtraction, Objectives After going throu...

Objectives After going through this unit, you should be able to 1. explain the processes involved ih addition and subtraction; 2. plan and execute activities that woul

Erp for a company, recomendation to a company to implement ERP to succeed

recomendation to a company to implement ERP to succeed

Number sequence, what is the formula to find a sequence on a string of numb...

what is the formula to find a sequence on a string of numbers?

Example of least common denominator, Example of Least Common Denominator: ...

Example of Least Common Denominator: Example: Add 1/7 +2 /3 + 11/12 + 4/6 Solution: Step 1:             Find out primes of each denominator. 7 = 7 (already is

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