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

Matrix, how to solve for x

how to solve for x

Calculate values of kinetics , A reaction following first-order kinetics wa...

A reaction following first-order kinetics was studied by determining the reactant concentrations at equal time intervals. Each successive pair of concentrations, [A] o and [A] 1

Shares and divident, A man invest ?13500 partly in shares paying 6% at ?140...

A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?

If a sequence is bounded and monotonic then it is convergent, Theorem ...

Theorem If {a n } is bounded and monotonic then { a n } is convergent.  Be cautious to not misuse this theorem.  It does not state that if a sequence is not bounded and/or

Ratio test - sequences and series, Ratio Test In this part we are goin...

Ratio Test In this part we are going to take a look at a test that we can make use to see if a series is absolutely convergent or not.  Remind that if a series is absolutely c

Area of regular polygon, Suppose a  regular polygon , which is an N-sided w...

Suppose a  regular polygon , which is an N-sided with equal side lengths S and similar angles at each corner. There is an  inscribed circle  to the polygon that has center C and ba

Union operations using union by weight, Show the result of the following se...

Show the result of the following sequence of UNION operations using union-by-weight with the following assumptions Unions are performed on the representatives on the sets th

First order differential equations, In this section we will consider for so...

In this section we will consider for solving first order differential equations. The most common first order differential equation can be written as: dy/dt = f(y,t) As we wil

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