Investigation Consider the function f ( x ) = 2 x n x 4 + 1 for nonnegative integer values of n . (a) Discuss the relationship between the value of n and the symmetry of the graph. (b) For which values of n will the x-axis be the horizontal asymptote? (c) For which value of n will y = 2 be the horizontal asymptote? (d) What is the asymptote of the graph when y = 2 (e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph. n 0 1 2 3 4 5 M N
Investigation Consider the function f ( x ) = 2 x n x 4 + 1 for nonnegative integer values of n . (a) Discuss the relationship between the value of n and the symmetry of the graph. (b) For which values of n will the x-axis be the horizontal asymptote? (c) For which value of n will y = 2 be the horizontal asymptote? (d) What is the asymptote of the graph when y = 2 (e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph. n 0 1 2 3 4 5 M N
Solution Summary: The author explains how to determine the relation between the symmetry of the function f(x) and the value of n.
(a) Discuss the relationship between the value of n and the symmetry of the graph.
(b) For which values of n will the x-axis be the horizontal asymptote?
(c) For which value of n will
y
=
2
be the horizontal asymptote?
(d) What is the asymptote of the graph when
y
=
2
(e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph.
A 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.
Explain the focus and reasons for establishment of 12.4.1(root test) and 12.4.2(ratio test)
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