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

Shares and divident, A man invest ?13500 partly in shares paying 6% at ?140...

A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?

An amortization, Ahmad borrowed $450000.00 at 3% compounded semi-annually f...

Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se

Compositions of relations, Let Consider R A Χ B, S B Χ C be two relation...

Let Consider R A Χ B, S B Χ C be two relations. Then compositions of the relations S and R given by SoR A Χ C and is explained by (a, c) €(S o R) iff € b € B like (a, b) € R,

Lattice or complement lattice, Let  be the set of all divisors of n. Constr...

Let  be the set of all divisors of n. Construct a Hasse diagram for D15, D20,D30. Check whether it is a lattice Or Complement lattice.

#title, how do you do hard math!!!

how do you do hard math!!!

Y=Theea[sin(inTheeta)+cos(inTheeta)], Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷d...

Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷dθ. Solution)  Y=θ[SIN(INθ)+COS(INθ)] applying u.v rule then dy÷dθ={[ SIN(INθ)+COS(INθ) ] dθ÷dθ }+ {θ[ d÷dθ{SIN(INθ)+COS(INθ) ] }    => SI

Using a number strip substract , Another aid that can help children pract...

Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means

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