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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.
Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +
Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ???? ????? bisects ??????? Prove: ??????? is a rt. ?
If x = b y where both b > 0, x > 0, then we define y = log b x, which is read as "y is the log to the base b of x". This means that, log b x or y is the number to
PROBLEMS RELATED TO APPLYING OPERATIONS : Some of us were testing Class 4 children with addition and subtraction problems. We gave them sums that were written horizontally and th
Vector Function The good way to get an idea of what a vector function is and what its graph act like is to look at an instance. Thus, consider the following vector function.
What is Markov Chains or Processes?
The area of a parallelogram can be expressed as the binomial 2x 2 - 10x. Which of the following could be the length of the base and the height of the parallelogram? To ?nd out
2.46825141458*1456814314.446825558556
In a parallelogram ABCD AB=20cm and AD=12cm.The bisector of angle A meets DC at E and BC produced at F.Find the length of CF.
lbl 2 lcl 2 sin 2 θ
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