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 +
Leading term 3x17
Leading coeﬃcient 3
Constant term 1
As x → −∞, f (x) → −∞
As x → ∞, f (x) → ∞ 1
3 (d) s(t) = −4.9t2 + v0 t + s0
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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