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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.
If a triangular sail has a horizontal length of 30 ft and a vertical height of 83 ft , Determine the area of the sail? a. 1,245 ft 2 b. 1,155 ft 2 c. 201 ft 2 d. 2,4
Quotient Rule : If the two functions f(x) & g(x) are differentiable (that means the derivative exist) then the quotient is differentiable and,
Certain model of new home distributed with a mean of $150,000. Find percentage of buyers who paid between $150,000-155,000 if standard deviation is $1800.
Which general famously stated 'I shall return'? A. Bull Halsey B. George Patton C. Douglas MacArthur D. Omar Bradley
The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable
Q. Find Common Denominators? What does it mean? Say you have two fractions, like 1/3 and 8/21 And they have different denominators (3 and 21). Sometimes, you'd prefer
railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel
By such interactions children learn to articulate reasons and construct arguments. When a child is exposed to several interactions of this kind, she gradually develops the ability
Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t
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