5 Steps to a 5: AP Calculus AB 2022 by William Ma

Author:William Ma
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2021-08-15T00:00:00+00:00

Figure 8.8-9

Enter y 1 = cos(x2)

Using the [Inflection] function of your calculator, you obtain three points of inflection on [0, π]. The points of inflection occur at x = 1.35521, 2.1945, and 2.81373. Since y1 = cos(x2) is an even function, there is a total of 6 points of inflection on [-π, π]. An alternate solution is to enter The graph of y2 indicates that there are 6 zeros on [-π, π].

19. Enter y 1 = 3 ∗ e ∧ (-x ∧ 2/2). Note that the graph has a symmetry about the y -axis. Using the functions of the calculator, you will find:

(a) a relative maximum point at (0, 3), which is also the absolute maximum point;

(b) points of inflection at (-1, 1.819) and (1, 1.819);

(c) y = 0 (the x -axis) a horizontal asymptote;

(d) y1 increasing on (-∞, 0] and decreasing on [0, ∞); and

(e) y1 concave upward on (-∞, -1) and (1, ∞) and concave downward on (-1, 1). (See Figure 8.8-10.)

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