Stitz-Zeager_College_Algebra_e-book

G can an x intercept yield a local extrema can it

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Unformatted text preview: c) = 0. If c2 − 2 = 0 then c = ± 2. Since c is between 1 and 3, c is √ positive, so c = 2. Our primary use of the Intermediate Value Theorem is in the construction of sign diagrams, as in Section 2.4, since it guarantees us that polynomial functions are always positive (+) or always negative (−) on intervals which do not contain any of its zeros. The general algorithm for polynomials is given below. 186 Polynomial Functions Steps for Constructing a Sign Diagram for a Polynomial Function Suppose f is a polynomial function. 1. Find the zeros of f and place them on the number line with the number 0 above them. 2. Choose a real number, called a test value, in each of the intervals determined in step 1. 3. Determine the sign of f (x) for each test value in step 2, and write that sign above the corresponding interval. Example 3.1.5. Construct a sign diagram for f (x) = x3 (x − 3)2 (x + 2) x2 + 1 . Use it to give a rough sketch of the graph of y = f (x). Solution. First, we find the zeros of f by solving x3 (...
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