Unformatted text preview: ﬁnd the only one zero of f , x = 2 . This one x value divides the number line into two
3
intervals, from which we choose x = 0 and x = 1 as test values. We ﬁnd f (0) = 4 > 0 and
f (1) = 1 > 0. Since we are looking for solutions to 9x2 − 12x + 4 ≤ 0, we are looking for 2.4 Inequalities 163 x values where 9x2 − 12x + 4 < 0 as well as where 9x2 − 12x + 4 = 0. Looking at our sign
diagram, there are no places where 9x2 − 12x + 4 < 0 (there are no (−)), so our solution
2
is only x = 3 (where 9x2 − 12x + 4 = 0). We write this as 2 . Graphically, we solve
3
9x2 + 4 ≤ 12x by graphing g (x) = 9x2 + 4 and h(x) = 12x. We are looking for the x values
where the graph of g is below the graph of h (for 9x2 + 4 < 12x) and where the two graphs
2
intersect (9x2 + 4 = 12x). We see the line and the parabola touch at 3 , 8 , but the parabola
3
is always above the line otherwise.
y
13
12
11
10 (+)
0 0
2
3 9 (+) 8
7
6 1 5
4
3
2
1
−1 1 x 4. To solve our last inequality, 2x ...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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