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

Class 10, The value of K for (k+1)x^2-2(k-1)x+1 = 0 has real and equal root...

The value of K for (k+1)x^2-2(k-1)x+1 = 0 has real and equal roots.

Find the probability , 1.  What is the probability that the two beverages w...

1.  What is the probability that the two beverages will be of the same kind? 2.  What is the probability that the two beverages will be different? 3.  What is the probability

Expected value, Expected Value For taking decisions under conditions of...

Expected Value For taking decisions under conditions of uncertainty, the concept of expected value of a random variable is used. The expected value is the mean of a probability

#algebra 2 .., encoded with the matrix -3 -7 and 4 9. what lights up a socc...

encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)

Statistics and probability, STATISTICS AND PROBABILITY : Statistics  ar...

STATISTICS AND PROBABILITY : Statistics  are the  only  tools  by  which  an  opening  can  be  cut  through  the formidable  thicket  of difficulties  that bars the  path  of

Addition involving negative numbers, Q. Addition Involving Negative Numbers...

Q. Addition Involving Negative Numbers? Ans. When you add together positive and negative numbers, there are essentially three possibilities that you can encounter. Let's e

Describe the laws of sines, Q. Describe the Laws of Sines? Ans. Up...

Q. Describe the Laws of Sines? Ans. Up to now we have dealt exclusively with right triangles.  The Law of Sines and the Law of Cosines are used to solve  oblique triangles

How will the decimal point move when 245.398 is multiplied, How will the de...

How will the decimal point move when 245.398 is multiplied by 100? It is moved two places to the right. While multiplying by multiples of 10, the decimal point is moved to the

Area of a circle, There's a nice way to show why the expresion for the area...

There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of 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