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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.

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.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.CR: Chapter Review
Problem 1CC
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x3 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.
Transcribed Image Text:x3 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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