Consider the function f(x) = x² + 7x + 13 x + 4 (a) Find the domain and intercepts of f. (b) Find f'(x). (c) Find the coordinates of any stationary points of f. Construct a table of signs for f'(x), determine the intervals on which ƒ is increasing and those on which f is decreasing, and determine the nature(s) of the stationary point(s).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the function f(x) =
x² + 7x + 13
x +4
(a) Find the domain and intercepts of f.
(b) Find f'(x).
(c) Find the coordinates of any stationary points of f. Construct a table of
signs for f'(x), determine the intervals on which f is increasing and
those on which f is decreasing, and determine the nature(s) of the
stationary point (s).
(d) Determine the equations of the asymptotes of f.
(e) Determine whether f is an even or odd function, or neither.
(f) Hence sketch the graph of ƒ.
Transcribed Image Text:Consider the function f(x) = x² + 7x + 13 x +4 (a) Find the domain and intercepts of f. (b) Find f'(x). (c) Find the coordinates of any stationary points of f. Construct a table of signs for f'(x), determine the intervals on which f is increasing and those on which f is decreasing, and determine the nature(s) of the stationary point (s). (d) Determine the equations of the asymptotes of f. (e) Determine whether f is an even or odd function, or neither. (f) Hence sketch the graph of ƒ.
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