Question

In: Advanced Math

2. For the curve y = 3x / x^2-1 determine each of the following and use...

2. For the curve y = 3x / x^2-1 determine each of the following and use all of the information to draw its graph

and notate the information on it.
(a) Find the domain of the function, as well as any x or y intercepts and symmetry.

(b) Find all vertical (2 of them) and horizontal (1) asymptotes. Support your work with limits.

(c) Use the first derivative to determine the maximums, minimums and intervals of increase/decrease of f(x).

(d) Use the second derivative to determine the points of inflection and intervals of concavity of f(x).

(e) Sketch the graph of f(x) and annotate it as follows: Sketch the asymptotes as dashed lines.

Plot and label the maxes (M), mins (m) inflection points (IP) on the graph.

Label the intervals on the graph for each of the 4 types of basic shapes:
1 for concave up/inc
2 for concave up/dec

3 for concave down/inc

4 for concave down/dec

Solutions

Expert Solution

Colby Messinger answered 1 year ago
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