Recognizes the absolute extrema & relative extrema for the following function.

                          f ( x ) = x²      on [-1, 2]

Solution:  As this function is simple enough to graph let's do that.  Though, we only want the graph on the interval [-1,2].  Here is the graph,

Note as well that we utilized dots at the end of the graph to remind us that the graph ends at these points.

Now we can identify the extrema from the graph.  It looks like we've got a relative & absolute minimum of zero at x = 0 and an absolute maximum of four at x = 2 . Note as well that x = -1 is not a relative maximum as it is at the ending point of the interval.

This function doesn't contain any relative maximums.

As we saw in the previous example functions do not have to have relative extrema.  It is entirely possible for a function to not have a relative maximum and/or a relative minimum.

Posted Date: 4/12/2013 5:43:59 AM | Location : United States

Ask an Expert

Related Discussions:- Recognizes the absolute extrema & relative extrema, Assignment Help, Ask Question on Recognizes the absolute extrema & relative extrema, Get Answer, Expert's Help, Recognizes the absolute extrema & relative extrema Discussions

Write discussion on Recognizes the absolute extrema & relative extrema
Your posts are moderated

Write your message here..

Related Questions

Introduction to multiplication and division, INTRODUCTION :  When a Class ... INTRODUCTION :  When a Class 5 child was given the problem 'If I paid Rs. 60 for 30 pencil boxes, how much did b pencil box cost?', he said it would be 60 x 30 = 1800. This

Micrometer, how to use a micrometer how to use a micrometer

Mensuration, How do mensuration relate to the real life issues How do mensuration relate to the real life issues

Show that 8 - 10 + 21= 0, If A, B and P are the points (-4, 3), (0, -2) and... If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans :   AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2

Superimpose the three curves on the one axis, Submit solutions for all of t... Submit solutions for all of the following questions. Remember to set out your answers showing all steps completely and explicitly justify your steps. 1. Provide, in no more than

Kara brought $23 with her when she went shopping, Kara brought $23 with her... Kara brought $23 with her when she went shopping. She spent $3.27 for lunch and $14.98 on a shirt. How much money does she have left? The two items that Kara bought must be sub

the word rotor, a)    A palindrome is a word that reads the similar whethe... a)    A palindrome is a word that reads the similar whether read from right to left or from the left to right, the word ROTOR, for example. Let  be the number of words of length n,

Write down those features of such interactions, After seeing some children ... After seeing some children interacting naturally, write down those features of such interactions that make peer learning potentially a better way of learning. Another point that

Line of symmetry, how do I do it. how do I do it.

Time=distance/speed, time=2.82/4000 time=2.82/4000