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 [4 Marks] 6 y 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 1. Considering the following graph of f(x). + -2- 0 -2 4 6 i. Circle the interval(s) where f'(x) is positive. a) (-infinity, 0), (2, 4) c) (1, 3), (4, 4.5) b) (-infinity, 1), (3, 4.5) d) (3,2), (2,5) ii. Circle the interval(s) where f'(x) is negative. a) (0, 1), (4.5, 6) b) (0, 2), (4, 4.5), (4.5, 6) c) (-infinity, 1), (3, 4.5), (5, 6) d) (-infinity, -3), (4.5, 6)
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 [4 Marks] 6 y 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 1. Considering the following graph of f(x). + -2- 0 -2 4 6 i. Circle the interval(s) where f'(x) is positive. a) (-infinity, 0), (2, 4) c) (1, 3), (4, 4.5) b) (-infinity, 1), (3, 4.5) d) (3,2), (2,5) ii. Circle the interval(s) where f'(x) is negative. a) (0, 1), (4.5, 6) b) (0, 2), (4, 4.5), (4.5, 6) c) (-infinity, 1), (3, 4.5), (5, 6) d) (-infinity, -3), (4.5, 6)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 50E
Related questions
Question
![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 [4 Marks]
6
y
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
X
>
+6
14
4
6
8
1
f"(x) > 0 for x<-2, 0<x<2
f"(x) <0 for -2<x<0, x>2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2Fab3d9f9e-6155-489f-86df-e3cf875f19d8%2F3mw22i3_processed.png&w=3840&q=75)
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 [4 Marks]
6
y
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
X
>
+6
14
4
6
8
1
f"(x) > 0 for x<-2, 0<x<2
f"(x) <0 for -2<x<0, x>2
Transcribed Image Text:1. Considering the following graph of f(x).
+
-2-
0
-2
4
6
i. Circle the interval(s) where f'(x) is positive.
a) (-infinity, 0), (2, 4)
c) (1, 3), (4, 4.5)
b) (-infinity, 1), (3, 4.5)
d) (3,2), (2,5)
ii. Circle the interval(s) where f'(x) is negative.
a) (0, 1), (4.5, 6)
b) (0, 2), (4, 4.5), (4.5, 6)
c) (-infinity, 1), (3, 4.5), (5, 6)
d) (-infinity, -3), (4.5, 6)
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
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning