Communication True or False: 7. The points of inflection are found by solving the first derivative equal to zero. 8. When the denominator of a rational function is zero the function will always have a vertical asymptote. 9. To determine the behavior of a function near the vertical asymptotes we use left and right hand limits. 10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test. 11. A function can never cross asymptotes. 12. To determine the end behavior of a function we must check the lim x →±xx 13. Sketch a graph of a rational function that satisfies the following conditions [ 6 y X f(0) = 0, f(-4) = 2, f(4) = -2 f(x) is undefined for x = ±2 f'(-4)= f'(0) = f '(4) = 0 f'(x) <0 for x<-4, x>4 f'(x)>0 for -4 +6 14 4 6 8 1 f"(x) > 0 for x<-2, 02
Communication True or False: 7. The points of inflection are found by solving the first derivative equal to zero. 8. When the denominator of a rational function is zero the function will always have a vertical asymptote. 9. To determine the behavior of a function near the vertical asymptotes we use left and right hand limits. 10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test. 11. A function can never cross asymptotes. 12. To determine the end behavior of a function we must check the lim x →±xx 13. Sketch a graph of a rational function that satisfies the following conditions [ 6 y X f(0) = 0, f(-4) = 2, f(4) = -2 f(x) is undefined for x = ±2 f'(-4)= f'(0) = f '(4) = 0 f'(x) <0 for x<-4, x>4 f'(x)>0 for -4 +6 14 4 6 8 1 f"(x) > 0 for x<-2, 02
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter17: Statistical Thermodynamics: Introduction
Section: Chapter Questions
Problem 17.11E
Related questions
Question
Transcribed Image Text:Communication
True or False:
7. The points of inflection are found by solving the first derivative equal to zero.
8. When the denominator of a rational function is zero the function will always
have a vertical asymptote.
9. To determine the behavior of a function near the vertical asymptotes we use left
and right hand limits.
10. Determining if a local extrema is a maximum or minimum cannot be done
using the second derivative test.
11. A function can never cross asymptotes.
12. To determine the end behavior of a function we must check the lim
x →±xx
13. Sketch a graph of a rational function that satisfies the following conditions [
6
y
X
f(0) = 0, f(-4) = 2, f(4) = -2
f(x) is undefined for x = ±2
f'(-4)= f'(0) = f '(4) = 0
f'(x) <0 for x<-4, x>4
f'(x)>0 for -4<x<-2, -2<x<0 and
0<x<2,2<4
f"(0) = 0
>
+6
14
4
6
8
1
f"(x) > 0 for x<-2, 0<x<2
f"(x) <0 for -2<x<0, x>2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
Principles of Modern Chemistry
Chemistry
ISBN:
9781305079113
Author:
David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:
Cengage Learning
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
Principles of Modern Chemistry
Chemistry
ISBN:
9781305079113
Author:
David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:
Cengage Learning