Stitz-Zeager_College_Algebra_e-book

# We can verify our handiwork using the techniques

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Unformatted text preview: x2 − 399x + 90 (n) p(x) = 9x3 − 5x2 − x 7 1 1 2. Find the real zeros of f (x) = x3 − 12 x2 − 72 x + 72 by ﬁrst ﬁnding a polynomial q (x) with integer coeﬃcients such that q (x) = N · f (x) for some integer N . (Recall that the Rational Zeros Theorem required the polynomial in question to have integer coeﬃcients.) Show that f and q have the same real zeros. 3. Solve the polynomial inequality and give your answer in interval form. (a) −2x3 + 19x2 − 49x + 20 > 0 (e) 4x3 ≥ 3x + 1 (b) x4 − 9x2 ≤ 4x − 12 (f) (c) (x − 1)2 ≥ 4 (g) (d) 7 −5x3 + 35x2 − 45x − 25 > 0 x3 +2x2 <x+2 2 4 ≤ 16 + 4x − x x3 (h) 3x2 + 2x < x4 4. Let f (x) = 5x7 − 33x6 + 3x5 − 71x4 − 597x3 + 2097x2 − 1971x + 567. With the help of your classmates, ﬁnd the x- and y - intercepts of the graph of f . Find the intervals on which the function is increasing, the intervals on which it is decreasing and the local extrema. Sketch the graph of f , using more than one picture if necessary to show all of the important features of the graph....
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