Recognizes the absolute extrema & relative extrema, Mathematics

Assignment Help:

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.


Related Discussions:- Recognizes the absolute extrema & relative extrema

Share and dividend, give me a proper project on share and dividend of minim...

give me a proper project on share and dividend of minimum 25 pages

Equations, 20 equations that equal 36

20 equations that equal 36

Find the coordinates of the point p, Find the coordinates of the point P wh...

Find the coordinates of the point P which is three -fourth of the way from A (3, 1) to B (-2, 5).

Uniform distribution over the interval, High temperatures in certain city i...

High temperatures in certain city in the month of August follow uniform distribution over the interval 60-85 F. What is probability that a randomly selected August day has a Temper

Duality., advanteges of duality

advanteges of duality

Integers, What are some equations for 36?

What are some equations for 36?

Formula to computing how much lumber to buy, Audrey is creating a increased...

Audrey is creating a increased flowerbed which is 4.5 ft by 4.5 ft. She requires computing how much lumber to buy. If she requires knowing the distance around the flowerbed, which

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