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We notice that k ( x) = 3x 2 + 6x 9 = 3( x 1) ( x + 3) . So the sign of k changes at x = 1 and x = 3. We conclude that k is positive when x < 3; k is negative when 3 < x < 1; k is positive when x > 3. Finally, k ( x) = 6x + 6. Thus the graph is concave down when x < 1 and the graph is concave up when x > 1. Putting all this information together, and using the facts that k( x) when x and k( x) + when x + , we obtain the graph shown in Figure 3.8.

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A namespace is declared using the namespace keyword. The general form of namespace is shown here: namespace name { // members } Here, name is the name of the namespace. A namespace declaration defines a scope. Anything declared immediately inside the namespace is in scope throughout the namespace. Within a namespace, you can declare classes, structures, delegates, enumerations, interfaces, or another namespace. Here is an example of a namespace that creates a namespace called Counter. It localizes the name used to implement a simple countdown counter class called CountDown.

Here is the second variation for the balance sheet balancing. Having made a big fuss about static and dynamic numbers, this second method makes no distinction between static and dynamic numbers. It uses the difference between Total assets and Total liabilities Shareholders equity, but in a way that does not lead to the flip-flops.

We use the Fundamental Theorem. In this example, f ( x) = x 2 . We need to find an antiderivative F . From our experience in Section 4.1, we can determine that F ( x) = x 3 /3 will do. Then, by the Fundamental Theorem of Calculus,

The function is continuous to zero from the right side but not from the left side. The cube root function, y = &,behaves differently. There are real cube roots of both positive and negative numbers as well as zero. This function is continuous over the entire range of real numbers for x .

Thermostats exist so that the furnace or air conditioner knows to kick in when a certain temperature level has been breached. Thanks to thermostats, you don t