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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 .
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.
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?
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
Can Slope is calculated as run-rise?
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,
(4 sqrt3+5 sqrt2)/(sqrt48+ srt18)
78,990
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.
how do you do hard math!!!
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
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
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