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Stitz-Zeager_College_Algebra_e-book

# 202 polynomial functions example 322 let px 2x3 5x

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Unformatted text preview: can it have? (b) Could a polynomial have two local maxima but no local minima? (c) If a polynomial has two local maxima and two local minima, can it be of odd degree? Can it be of even degree? (d) Can a polynomial have local extrema without having any real zeros? (e) Why must every polynomial of odd degree have at least one real zero? (f) Can a polynomial have two distinct real zeros and no local extrema? (g) Can an x-intercept yield a local extrema? Can it yield an absolute extrema? (h) If the y -intercept yields an absolute minimum, what can we say about the degree of the polynomial and the sign of the leading coeﬃcient? 3.1 Graphs of Polynomials 3.1.2 193 Answers √ 1. (a) f (x) = 3x17 + 22.5x10 − πx7 + Degree 17 √ Leading term 3x17 √ Leading coeﬃcient 3 Constant term 1 3 As x → −∞, f (x) → −∞ As x → ∞, f (x) → ∞ 1 3 (d) s(t) = −4.9t2 + v0 t + s0 Degree 2 Leading term −4.9t2 Leading coeﬃcient −4.9 Constant term s0 As t → −∞, s(t) → −∞ As t → ∞, s(t) → −∞ (b) p(t) = −t2 (3 − 5t)(t2 + t +...
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