What is the lower bound of the polynomial function?
f(x) = x^4 − 4x^3 − 9x^2 + x − 16
are there several lower bounds?? thanks A LOT for your help!!!
+128472 x^4 - 4x^3 - 9x^2 + x -16
Take all the negative factors of p/q = -16/1 = -16 =
-1, -2, -4, -8, -16
We perform syntheteeic division.....if we have alternating signs on the bottom row, then we have a lower bound
-1 [ 1 - 4 - 9 1 -16 ]
- 1 5
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1 -5 -4 signs do not alternate
-2 [ 1 -4 -9 1 -16 ]
-2 12 -6 10
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1 -6 3 -5 -6 signs do not alternate
-4 [ 1 -4 -9 1 -16 ]
-4 32 -92 364
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1 -8 23 -91 348 signs alternate......-4 is a lower bound
-8 [ 1 -4 -9 1 -16 ]
-8 96 -696 5560
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1 -12 87 -695 5544 signs alternate.........-8 is a lower bound
-16 [ 1 - 4 -9 1 -16 ]
-16 320 -4976 79600
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1 -20 311 -4975 79584 signs alternate......-16 is a lower bound
Lower bounds = - 4 , -8 , -16
