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

Approximating definite integrals - integration techniques, Approximating De...

Approximating Definite Integrals - Integration Techniques In this section we have spent quite a bit of time on computing the values of integrals. Though, not all integrals can

The rank correlation coefficient (r), The Rank Correlation Coefficient (R) ...

The Rank Correlation Coefficient (R) Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among tw

Evaluating the function at the point of limit, Calculate the value of the f...

Calculate the value of the following limit. Solution: This first time through we will employ only the properties above to calculate the limit. Firstly we will employ prop

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Geometry, calculate the area of a trapezoid with height 8cm base 18cm and 9...

calculate the area of a trapezoid with height 8cm base 18cm and 9cm

Mashed patatos, I have 6 cups of patatos that I have to share with 13 frien...

I have 6 cups of patatos that I have to share with 13 friends write that as the nearest hundredth

Estimate root of given equations, The positive value of k for which x 2 +K...

The positive value of k for which x 2 +Kx +64 = 0 & x 2 - 8x + k = 0 will have real roots . Ans: x 2 + K x + 64 = 0 ⇒  b 2 -4ac > 0 K 2 - 256 > 0 K

Tutoring , hi, i was wondering how do you provide tutoring for math specifi...

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

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