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Stitz-Zeager_College_Algebra_e-book

# K list the local maximums if any exist l list the

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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 x-axis.) 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 x-axis.) 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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