Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: rmination of the zeros of f and their multiplicities, we know the graph crosses at x = − 26 ≈ −1.22 then turns back upwards to touch the x−axis at x = −1. This tells us that, despite what the calculator showed us the first time, there is a relative maximum occurring at x = −1 and not a ‘flattened crossing’ as we originally 210 Polynomial Functions believed. After resizing the window, we see not only the relative maximum but also a relative minimum just to the left of x = −1 which shows us, once again, that Mathematics enhances the technology, instead of vice-versa. Our next example shows how even a mild-mannered polynomial can cause problems. Example 3.3.4. Let f (x) = x4 + x2 − 12. 1. Use Cauchy’s Bound to determine an interval in which all of the real zeros of f lie. 2. Use the Rational Zeros Theorem to determine a list of possible rational zeros of f . 3. Graph y = f (x) using your graphing calculator. 4. Find all of the real zeros of f and their multiplicities. Solution. 1. Applying Cau...
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