Let f be the function defined by f(x): 1-2x² x²-1 (a) Determine the vertical and horizontal asymptotes (show all limits). (b) Use the sign pattern for f'(x) to determine (i) the interval(s) over which f rises and where it falls; (ii) the local extrema. (c) Use the sign pattern for f" to determine (i) where the graph of f is concave up and where it is concave down. (ii) the inflection points (if any)
Let f be the function defined by f(x): 1-2x² x²-1 (a) Determine the vertical and horizontal asymptotes (show all limits). (b) Use the sign pattern for f'(x) to determine (i) the interval(s) over which f rises and where it falls; (ii) the local extrema. (c) Use the sign pattern for f" to determine (i) where the graph of f is concave up and where it is concave down. (ii) the inflection points (if any)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let f be the function defined by
f(x)=
=
1-2x²
x²-1
(a) Determine the vertical and horizontal asymptotes (show all limits).
(b) Use the sign pattern for f(x) to determine
(i) the interval(s) over which f rises and where it falls;
(ii) the local extrema.
(c) Use the sign pattern for f" to determine
(i) where the graph of f is concave up and where it is concave down.
(ii) the inflection points (if any)
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