Let c>0 be a fixed number, and consider the function f(x)=- 6x² –c² Answer the following questions (some answers are to be given in terms of c). Make sure to show your work and justify your arguments. (a) Find the domain and the equations of the vertical asymptotes of f(x). (b) f(x) has exactly one oblique asymptote. Find its equation. (c) Find the x-coordinates of all critical points of f(x). (d) For each critical point, decide whether it is a maximum, minimum, or neither. (e) Use the results of the previous parts to draw (by hand) a sketch of the graph of f(x). Mark clearly asymptotes and extreme points.
Let c>0 be a fixed number, and consider the function f(x)=- 6x² –c² Answer the following questions (some answers are to be given in terms of c). Make sure to show your work and justify your arguments. (a) Find the domain and the equations of the vertical asymptotes of f(x). (b) f(x) has exactly one oblique asymptote. Find its equation. (c) Find the x-coordinates of all critical points of f(x). (d) For each critical point, decide whether it is a maximum, minimum, or neither. (e) Use the results of the previous parts to draw (by hand) a sketch of the graph of f(x). Mark clearly asymptotes and extreme points.
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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Let c>0 be a fixed number, and consider the function f(x)=-
6x2 -c2
Answer the following questions (some answers are to be given in terms of c).
Make sure to show your work and justify your arguments.
(a) Find the domain and the equations of the vertical asymptotes of f(x).
(b) f(x) has exactly one oblique asymptote. Find its equation.
(c) Find the x-coordinates of all critical points of f(x).
(d) For each critical point, decide whether it is a maximum, minimum, or neither.
(e) Use the results of the previous parts to draw (by hand) a sketch of the graph of f(x). Mark clearly asymptotes and extreme
points.
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