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

Trignometry, i have to get 10 points in 10th class

i have to get 10 points in 10th class

Rolle''s theorem, The curve (y+1) 2 =x 2 passes by the points (1, 0) and ...

The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that  dy dx  vanishes for some value of x in the interval -1≤x≤1?

Parallelogram, fig angles of a irregular polygons exterior and interior .

fig angles of a irregular polygons exterior and interior .

Numerical analysis and computer techniques, write a fortan programme to gen...

write a fortan programme to generate prime number between 1 to 100

Determine y' for xy = 1 by implicit differentiation, Determine y′ for xy = ...

Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem.  Just solve for y to

Divides a given line-segment externally in the ratio of 1:2, Divides a give...

Divides a given line-segment externally in the ratio of 1:2 Construction: i )Draw BX making an actueangle at B. ii) Starting from B, mark 2 equal points on BX as shown in the f

Least common denominator of rational expression, Perform the denoted operat...

Perform the denoted operation.                    (4/6x 2 )-(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus

Profit maximization, a medical clinic performs three types of medical tests...

a medical clinic performs three types of medical tests that use the same machines. Tests A, B,and C take 15 minutes, 30 minutes and 1 hours respectively, with respective profits of

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