Unformatted text preview: points with a y value of
1, as seen in the graph below. That means there are two solutions to f (x) = 1.
y
4
3
2
1 −4 −3 −2 −1 1 2 3 4 x −1
−2
−3
−4 9. As we move from left to right, the graph rises from (−4, −3) to (0, 3). This means f is
increasing on the interval [−4, 0]. (Remember, the answer here is an interval on the xaxis.)
10. As we move from left to right, the graph falls from (0, 3) to (4, −3). This means f is decreasing
on the interval [0, 4]. (Remember, the answer here is an interval on the xaxis.)
11. The function has its only local maximum at (0, 3).
12. There are no local minimums. Why don’t (−4, −3) and (4, −3) count? Let’s consider the
point (−4, −3) for a moment. Recall that, in the deﬁnition of local minimum, there needs to
be an open interval I which contains x = −4 such that f (−4) < f (x) for all x in I diﬀerent
from −4. But if we put an open interval around x = −4 a portion of that interval will lie
outside of the domain of f . B...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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