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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
Related questions
Question
![The image contains a piecewise function \( f(x) \) and a problem statement asking to find the value of \( c \) such that the function is continuous everywhere. The function is defined differently for values of \( x \) less than or equal to \( c \) and for values of \( x \) greater than \( c \).
Below is the complete transcription:
---
**Find \( c \) such that the function**
\[ f(x) = \begin{cases}
x^2 - 5 & \text{if } x \leq c \\
10x - 30 & \text{if } x > c
\end{cases} \]
**is continuous everywhere.**
\[ c = \ \underline{\hspace{2cm}} \]
---
This piecewise function has two different expressions: \( x^2 - 5 \) for \( x \leq c \) and \( 10x - 30 \) for \( x > c \). To find the value of \( c \) that makes \( f(x) \) continuous everywhere, the two expressions must meet at \( x = c \). This means that the limit from the left-hand side of \( c \) and the limit from the right-hand side of \( c \) must be equal, ensuring that there is no discontinuity at \( x = c \).
There were no graphs or diagrams included in the image that need further explanation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdccbde07-1885-4681-9cbb-26aa67baf026%2F9282263e-bcde-40a7-b835-27005fe9268b%2Fzqxk1fq_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a piecewise function \( f(x) \) and a problem statement asking to find the value of \( c \) such that the function is continuous everywhere. The function is defined differently for values of \( x \) less than or equal to \( c \) and for values of \( x \) greater than \( c \).
Below is the complete transcription:
---
**Find \( c \) such that the function**
\[ f(x) = \begin{cases}
x^2 - 5 & \text{if } x \leq c \\
10x - 30 & \text{if } x > c
\end{cases} \]
**is continuous everywhere.**
\[ c = \ \underline{\hspace{2cm}} \]
---
This piecewise function has two different expressions: \( x^2 - 5 \) for \( x \leq c \) and \( 10x - 30 \) for \( x > c \). To find the value of \( c \) that makes \( f(x) \) continuous everywhere, the two expressions must meet at \( x = c \). This means that the limit from the left-hand side of \( c \) and the limit from the right-hand side of \( c \) must be equal, ensuring that there is no discontinuity at \( x = c \).
There were no graphs or diagrams included in the image that need further explanation.
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 3 steps with 4 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,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
