Finding absolute extrema, Mathematics

Assignment Help:

Finding Absolute Extrema :Now it's time to see our first major application of derivatives.  Specified a continuous function, f(x), on an interval [a,b] we desire to find out the absolute extrema of the function. To do this we will requierd many of the ideas which we looked at in the previous section.

Firstly, as we have an interval and we are considering that the function is continuous the Extreme Value Theorem described that we can actually do this. it is a good thing of course. We don't desire to be trying to determine something that may not exist.

Next, we illustrated in the earlier section that absolute extrema can take place at endpoints or at relative extrema.  Also, from Fermat's Theorem we know that the list of critical points is also a list of all probable relative extrema.  Thus the endpoints along with the list of all critical points will actually be a list of all probable absolute extrema.

Now we just required to recall that the absolute extrema are nothing more than the largest & smallest values which a function will take thus all that we actually required to do is get a list of possible absolute extrema, plug these points into our function and then recognize the largest & smallest values.

 

 


Related Discussions:- Finding absolute extrema

Finish the work., six men and Eight boys can finish a piece of work in 14 d...

six men and Eight boys can finish a piece of work in 14 days while  eight men and twelve boys can do it in 10 days. Find the time taken by  1man alone and that by 1boy alone to fin

Semi-infinite slab solution in fourier number, Consider the temperature dis...

Consider the temperature distribution in a 1D flat plate, insulated at x = L and exposed to convective heat transfer at x = 0. On the axes below, sketch what the distribution looks

Calculate the density of people per square mile, 1.  In 1900, a certain cou...

1.  In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq

Divison, what is 24 diveded by 3

what is 24 diveded by 3

Rate of change interpretation of derivative, Rate of Change : The first in...

Rate of Change : The first interpretation of derivative is rate of change.  It was not the primary problem which we looked at in the limit chapter, however it is the most signific

Square of a number added to 25 equals 10 times the number, The square of a ...

The square of a number added to 25 equals 10 times the number. What is the number? Let x = the number.  The statement, "The square of a number added to 25 equals 10 times the n

Chi square distribution, Chi Square Distribution Chi square was first ...

Chi Square Distribution Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ 2 . This contains only one parameter, called the number of d

Find the function and domain, Consider the function f(x) = x + 1/x 2 + 2x ...

Consider the function f(x) = x + 1/x 2 + 2x - 3. (a) Find f(2) and f(-2). (b) Find the domain of f(x). (c) Does the range include 1? Show your working. (d) Find and si

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