2413labI5 - Laboratory I.5 Relationship between a Function...

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Laboratory I.5 Relationship between a Function and Its Derivative Goal • Given the graph of a function, to be able to visualize the graph of its derivative. Before the Lab In this laboratory, you will be asked to compare the graph of a function like the one in Figure 1 to that of its derivative. This exercise will develop your understanding of the geometric information that ƒ´ carries. Figure 1: f ( x ) = x 2 ( x – 1)( x + 1)( x + 2) You will need to bring an example of such a function into the lab with you, one whose graph meets the x -axis at four or five places over the interval [–3, 2] (see "Ready for Lab?"). During the lab, your partner will be asked to look at the graph of your function and describe the shape of its derivative (and you will be asked to do the same for your partner’s function). One way to make such a function is to write a polynomial in its factored form. For example, the function in Figure 1 in factored form is f ( x ) = x 2 ( x – 1)( x + 1)( x + 2). Its zeros are at 0 (twice), 1, –1, and –2. In the Lab (90 pts) 1. Author f(x) := x^ 2 (x^ 2 – 1)(x + 2) .

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MATH 2413 Lab 5 Page 2 of 4 a. Find the derivative of f . Use the command: Author f1(x) := dif(f(x),x). Plot the graphs of both f and f1 in the same viewing rectangle over the interval [–2.5,1.5]. In the rest of this lab, we will interchangeably use f1 and f ' to denote the derivative. Answer the following questions in interval notation by inspection of this graph. Record your answers in Derive Algebra window: b. Over what intervals does the graph of f appear to be rising as you move from left to right? c. Over what intervals does the graph of
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2413labI5 - Laboratory I.5 Relationship between a Function...

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