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OTake a Test Heidy Capote Google Chrome Secure https://www.mathxd.com/Student/Player Test aspx?testid 152222476¢enwin; yes Test: Test #4 (Sections 5.1 to 6.1) This Question: 1 pt For the polynoma function below (a) Listeach aealzero and its that the graph of f to large values (a) Find any real zeros off select comect doce below and, necessary OA The real zeroend tware Type an exact answer, using radicals needed Use wigors or factors for any murmeersinthe expression Uue a comma to aswersas B. There are no real zeros The mapacity of the larger zero is The multipliony of the smaller zero is the Kaais at the larger a-neeroese the xaxis at the smaller xnteropt The maimum number or turning points on ee gaph is (ype a whole number) resembles vaueserlel. ld) Trpe the power indton Click to select your Ask me anything OExplanation / Answer
We have f(x) = -8(x-2)(x+1)2
(a). The real zeros of f(x) are 2 and -1.The multiplicity of the larger zero (2) is 1. The multiplicity of the smaller zero (-1) is 2.
(c) We have f(x) = -8( x-2)( x2+2x+1) = -8( x3 +2x2+x – 2x2-4x -2) = -8(x3 -3x-2) = -8x3 +24x +16. Then f’(x) = -24x2 +24. Thus when f’(x) = 0, we have x2 = 1 or x = ±1. Thus x = ±1 are the critical points of f(x). Further, f’(0) = 24 and f’(-2) = -72. Thus -1 is a turning point. Also, f(2) = -72 and f(0) = 24 so that 1 is also a turning point. The graph has only 2 turning points.
(b) The x-intercepts are where y = 0. These are -1 and +2 . Since -1 is a turning point, the graph does not cross the X-Axis at x = -1 (smaller x-intercept). Since x = 2 is not a turning point, the graph crosses the X-Axis at x = 2(larger x-intercept).
(d) For large values of x, the graph of f(x) will resemble the graph of g(x) = -8x3.The required power function is y = g(x) = -8x3.
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