27_Cal_Solution of Calculus_6e

27_Cal_Solution of Calculus_6e - C01S03.032: The graph...

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Unformatted text preview: C01S03.032: The graph starts with two “bends” when c = −5. As c increases the bends become narrower and narrower and disappear when c = 0. Then the graph gets steeper and steeper. See the following figure. 15 c=5 c = –5 10 5 -4 -2 2 4 -5 -10 C01S03.033: The graph always passes through (0, 0) and is tangent to the x-axis there. When c = −5 there is another zero at x = 5. As c increases this zero shifts to the left until it coincides with the one at x = 0 when c = 0. At this point the “bend” in the graph disappears. As c increases from 1 to 5, the bend reappears to the left of the x-axis and the second zero reappears at −c. C01S03.034: The graph is always tangent to the x-axis at x = 0 and is always symmetric around the y -axis. When c = −5 there is another pair of zeros near ± 2.2. As c increases these zeros move closer to x = 0 and the bends in the graph get smaller and smaller. They disappear when c = 0 and, at the same time, the zeros merge with the one at x = 0. Thereafter the graph simply becomes steeper and steeper. See the following figure. c=5 15 10 5 c = –5 -3 -2 -1 1 2 3 -5 C01S03.035: The graph is always symmetric around the origin (and, consequently, always passes through the origin). When c = −5 there is another pair of zeros near ± 2.2. As c increases the graph develops positive slope at x = 0, two more bends, and two more zeros on either side of the origin. They move outward and, when c = −2, they coincide with the outer pair of zeros, which have also been moving toward the origin. They reach the origin when c = 0 and thereafter the graph simply becomes steeper and steeper. C01S03.036: As c increases the “mountain” around the y -axis gets narrower and steeper. See the following 4 ...
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