Use the table below to find X f'(x) g'(x) 1 2 1 [1.3f(x)] |x = 5 = 253 1 [1.3f(x)] dx 3 4 1 2 لی اند 3 4 |x=5 545 (Type an integer or a decimal.)
Use the table below to find X f'(x) g'(x) 1 2 1 [1.3f(x)] |x = 5 = 253 1 [1.3f(x)] dx 3 4 1 2 لی اند 3 4 |x=5 545 (Type an integer or a decimal.)
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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![### Problem Statement
Use the table below to find \( \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} \).
### Table
| \( x \) | 1 | 2 | 3 | 4 | 5 |
|---------|---|---|---|---|---|
| \( f'(x) \) | 2 | 5 | 3 | 1 | 4 |
| \( g'(x) \) | 1 | 3 | 4 | 2 | 5 |
### Solution
Calculate \( \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} \).
\[ \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} \]
To find this derivative, use the constant multiple rule, which states that the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.
Thus:
\[ \frac{d}{dx}[1.3f(x)] = 1.3 \cdot f'(x) \]
Substitute \( x = 5 \) into the equation:
\[ \left. 1.3 \cdot f'(x) \right|_{x=5} = 1.3 \cdot f'(5) \]
From the table, \( f'(5) = 4 \).
Therefore:
\[ 1.3 \cdot 4 = 5.2 \]
### Final Answer
\[ \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} = 5.2 \]
(Type an integer or a decimal.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F982437f2-81fd-4f07-8f8a-fea4c039ac1e%2F2656e015-09b3-4de3-b698-6e1702fe491f%2Fkprjhxq_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Use the table below to find \( \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} \).
### Table
| \( x \) | 1 | 2 | 3 | 4 | 5 |
|---------|---|---|---|---|---|
| \( f'(x) \) | 2 | 5 | 3 | 1 | 4 |
| \( g'(x) \) | 1 | 3 | 4 | 2 | 5 |
### Solution
Calculate \( \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} \).
\[ \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} \]
To find this derivative, use the constant multiple rule, which states that the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.
Thus:
\[ \frac{d}{dx}[1.3f(x)] = 1.3 \cdot f'(x) \]
Substitute \( x = 5 \) into the equation:
\[ \left. 1.3 \cdot f'(x) \right|_{x=5} = 1.3 \cdot f'(5) \]
From the table, \( f'(5) = 4 \).
Therefore:
\[ 1.3 \cdot 4 = 5.2 \]
### Final Answer
\[ \left. \frac{d}{dx}[1.3f(x)] \right|_{x=5} = 5.2 \]
(Type an integer or a decimal.)
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