Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
if possible, find the value of the constant c that makes the function f continous at every point.
![The image presents a mathematical problem that involves finding a constant \( c \) that makes the function \( f \) continuous at a certain point. The function \( f(x) \) is defined piecewise as follows:
\[
f(x) =
\begin{cases}
cx^2 + 3x - 1, & x < 4 \\
x^3 + cx, & x \geq 4
\end{cases}
\]
This problem is from the field of calculus, specifically focusing on the concept of continuity at a point. In order to make \( f \) continuous at \( x = 4 \), the left-hand limit, the right-hand limit, and the value of the function at \( x = 4 \) must all be equal.
No graphs or diagrams are included in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5f867ce-3ef7-4295-bb9e-df96fc34dcce%2Fe530c195-3a3a-4944-b4be-b777f741702f%2F3w01e8b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical problem that involves finding a constant \( c \) that makes the function \( f \) continuous at a certain point. The function \( f(x) \) is defined piecewise as follows:
\[
f(x) =
\begin{cases}
cx^2 + 3x - 1, & x < 4 \\
x^3 + cx, & x \geq 4
\end{cases}
\]
This problem is from the field of calculus, specifically focusing on the concept of continuity at a point. In order to make \( f \) continuous at \( x = 4 \), the left-hand limit, the right-hand limit, and the value of the function at \( x = 4 \) must all be equal.
No graphs or diagrams are included in the image.
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