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

Shares and dividends, How do I proceed with a project on Shares and Dividen...

How do I proceed with a project on Shares and Dividends?

Math, what is quantity ?

what is quantity ?

Find the radius of the inner circle, The area enclosed between two concentr...

The area enclosed between two concentric circles is 770cm 2 . If the radius of the outer circle is 21cm, find the radius of the inner circle. (Ans :14cm) Ans: Π R 2 - Π r 2 =

Definition of minimum and maximum values, Definition 1.   We say that f...

Definition 1.   We say that f(x) consist an absolute (or global) maximum at x = c if f ( x ) ≤ f (c ) for every x in the domain we are working on. 2.  We say that at x = c ,

Advantages and disadvantages of decision trees, Advantages of decision tree...

Advantages of decision trees 1. This clearly brings out implicit calculations and assumptions for all to see question and revise 2. This is simple to understand Disadvan

Without a calculator give the exact value, without a calculator give the ex...

without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1  (e)  Solution (b) log10

Slope-intercept form, Slope-intercept form The ultimate special form of...

Slope-intercept form The ultimate special form of the equation of the line is possibly the one that most people are familiar with.  It is the slope-intercept form.  In this if

Compute the double integral - triangle with vertices, 1) let R be the trian...

1) let R be the triangle with vertices (0,0), (pi, pi) and (pi, -pi). using the change of variables formula u = x-y and v = x+y , compute the double integral (cos(x-y)sin(x+y) dA a

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