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

#titl., class 10 Q.trigonometric formula of 1 term

class 10 Q.trigonometric formula of 1 term

Core concepts, Discuss mareketing core concepts analysing how they are used...

Discuss mareketing core concepts analysing how they are used in marketing hospitality product

How much area will it irrigate in 30 minutes , Water in a canal 30 dm wide ...

Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?

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

Find the maxima or minima and green theorem, 1) find the maxima and minima ...

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

Limits at infinity, Limits At Infinity, Part I : In the earlier section w...

Limits At Infinity, Part I : In the earlier section we saw limits which were infinity and now it's time to take a look at limits at infinity.  Through limits at infinity we mean

Determine that the series is convergent or divergent, Determine or find out...

Determine or find out if the subsequent series is convergent or divergent.  If it converges find out its value. Solution To find out if the series is convergent we fir

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