The shape of a graph, part ii, Mathematics

Assignment Help:

The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function.  In this section we will look at the information which the second derivative of a function can give us a regarding the graph of a function.

Some definitions

Concavity: The main concept which we'll be discussing in this section is concavity.  Concavity is easiest to see with a graph .

899_concave.png

Concave up

A function is concave up if it "opens" up and

Concave down

The function is concave down if it "opens" down. 

Notice that concavity has not anything to do with increasing or decreasing.  Any function can be concave up and either increasing or decreasing.  Likewise, a function can be concave down and either increasing or decreasing.

It's possibly not the best way to described concavity by saying which way it "opens" since it is a somewhat nebulous definition.  Following is the mathematical definition of concavity.


Related Discussions:- The shape of a graph, part ii

Combination, three complain forces of magnitudes 20N 30N and 45N

three complain forces of magnitudes 20N 30N and 45N

Application of statistics-human resource management, Human resource managem...

Human resource management Statistics may be utilized in efficient employ of human resources for example we may provide questionnaires to workers to find out where the manageme

Trigonometry, If a+b+c = 3a , then cotB/2 cotC/2 is equal to

If a+b+c = 3a , then cotB/2 cotC/2 is equal to

Algebra, can I access algebra videos?

can I access algebra videos?

What is the value of the largest consecutive integer, The sum of three cons...

The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and

Gauss-siedel or newton-rapson method, A one-line diagram of a simple three-...

A one-line diagram of a simple three-bus power system is shown in Figure 1 with generation at bus 1. The magnitude of voltage at bus 1 is adjusted to 1.05 per unit. The scheduled l

Operations with rational numbers, larry spends 3/4 hours twice a day walkin...

larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?

Give the example of exponents, Give the example of Exponents? When a nu...

Give the example of Exponents? When a number is multiplied several times, it is easier to write it as an exponent. For example, four multiplied to itself three times, is writte

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