Recognizes the absolute extrema & relative extrema, Mathematics

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,

2291_maximum.png

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







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
Related Questions

Steps for Radio test Assume we have the series ∑a n Define, Then, a. If L b. If L>1 the series is divergent. c. If L = 1 the series might be divergent, this i

Find out the average temperature: Example: Find out the average temperature if the subsequent values were recorded: 600°F, 596°F, 597°F, 603°F Solution: Step


Give the Examples in Real World of Proportions? Proportions can be used in cooking. For example, the following is a set of ingredients for a pasta called "Spaghetti All' Amatri


hi, i was wondering how do you provide tutoring for math specifically discrete mathematics for computer science ? I want to get some help in understanding in the meantime about alg


The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin