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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.
Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form
(x+y+1)dy/dx=1
1+2cos(2x=0
joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
state tha different types of models used in operations research.
1. Finding the shortest path btween any two points on the surface of a sphere but use the method of the euler equations with an auxiliarty condition imposed? Question2:
Test Of Hypothesis On Proportions It follows a similar method to the one for means except that the standard error utilized in this case: Sp = √(pq/n) Z score is computed
How may six digit numbers can be made in which the sum of the digits is even? Ans = 9*10*10*10*10*5
4/x+4-3/x+3=2/x+2-1/x+1
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