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

Algebra 1, pls help me solve this step by step 6*11(7+3)/5-(6-4)

pls help me solve this step by step 6*11(7+3)/5-(6-4)

Calculus, sin(xy)+x=5y Find the derivative.

sin(xy)+x=5y Find the derivative.

Solving decimal equations, The distance around a square photograph is 12.8 ...

The distance around a square photograph is 12.8 centimeters. What is the langth of each side of the fotograph?

Find out the volume of the solid- method of rings, Find out the volume of t...

Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and  y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t

5th grade, 6 and 3/8 minus 1 and 3/4

6 and 3/8 minus 1 and 3/4

Show that positive integers is divisible by 6, Show that the product of 3 c...

Show that the product of 3 consecutive positive integers is divisible by 6. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1

Find out all the critical points and derivation, Find out all the critical ...

Find out all the critical points for the function. Solution Following is the derivative for this function. Now, this looks unpleasant, though along with a little fa

Find the average, The center of a national park is located at (0,0). A spec...

The center of a national park is located at (0,0). A special nature preserve is bounded by by straight lines connecting the points A at (3,2), B at (5,1), C at (8,4) and D at (6,5)

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