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Stitz-Zeager_College_Algebra_e-book

# C the maximums predicted by the three models are p2

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Unformatted text preview: tempt to determine the sign of f (−4), we are attempting to ﬁnd the sign of the number (−4)3 (−7)2 (−2), which works out to be (−)(+)(−) which is (+). If we move to the other side of x = −2, and ﬁnd the sign of f (−1), we are determining the sign of (−1)3 (−4)2 (+1), which is (−)(+)(+) which gives us the (−). Notice that signs of the ﬁrst two factors in both expressions are the same in f (−4) and f (−1). The only factor which switches sign is the third factor, (x + 2), precisely the factor which gave us the zero x = −2. If we move to the other side of 0 and look closely at f (1), we get the sign pattern (+1)3 (−2)2 (+3) or (+)(+)(+) and we note that, once again, going from f (−1) to f (1), the only factor which changed sign was the ﬁrst factor, x3 , which corresponds to the zero x = 0. Finally, to ﬁnd f (4), we substitute to get (+4)3 (+2)2 (+5) which is (+)(+)(+) or (+). The sign didn’t change for the middle factor (x − 3)2 . Even though this is the factor which corresponds to the zero x = 3, the fact that the quantity is squ...
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