Suppose f(x), f'(x), g(x), and g'(x) have the values shown: -6 I -7 f(x) -9 f'(x) -1 g(x) 10 g'(x) -4 Find the following. (fg)'(-7)= ()'(-) = 8 2 -9 10 -5 -8 -6 7 4 -4 -6 8 -6 10 -3 8 -4 -6 2
Suppose f(x), f'(x), g(x), and g'(x) have the values shown: -6 I -7 f(x) -9 f'(x) -1 g(x) 10 g'(x) -4 Find the following. (fg)'(-7)= ()'(-) = 8 2 -9 10 -5 -8 -6 7 4 -4 -6 8 -6 10 -3 8 -4 -6 2
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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![**Table Values for Functions and Their Derivatives**
Suppose \( f(x) \), \( f'(x) \), \( g(x) \), and \( g'(x) \) have the values shown in the table:
| \( x \) | \(-7\) | \(-6\) | \(-5\) | \(-4\) | \(-3\) |
|----------|--------|--------|--------|--------|--------|
| \( f(x) \) | \(-9\) | \( 8 \) | \(-8\) | \(-6\) | \(8\) |
| \( f'(x) \) | \(-1\) | \(2\) | \(6\) | \(8\) | \(4\) |
| \( g(x) \) | \(10\) | \(-9\) | \(7\) | \(-6\) | \(-6\) |
| \( g'(x) \) | \(4\) | \(10\) | \(4\) | \(10\) | \(2\) |
**Find the following:**
1. \( (fg)'(-7) \)
2. \( \left(\frac{f}{g}\right)'(-7) \)
### Explanation of Functions and Derivatives
- \( f(x) \) and \( g(x) \) represent the values of two functions at specific points.
- \( f'(x) \) and \( g'(x) \) represent the values of the derivatives of these functions at the same points.
### Calculations:
1. **Finding \( (fg)'(-7) \)**
Using the Product Rule for derivatives:
\[ (fg)'(x) = f'(x)g(x) + g'(x)f(x) \]
Substitute \( x = -7 \):
\[ (fg)'(-7) = f'(-7)g(-7) + g'(-7)f(-7) \]
\[ (fg)'(-7) = (-1)(10) + (4)(-9) \]
\[ (fg)'(-7) = -10 - 36 \]
\[ (fg)'(-7) = -46 \]
2. **Finding \( \left( \frac{f}{g](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdccbde07-1885-4681-9cbb-26aa67baf026%2F8ea14f32-5e5a-4073-af6d-2161bb22a52f%2Fc5dwq9r_processed.png&w=3840&q=75)
Transcribed Image Text:**Table Values for Functions and Their Derivatives**
Suppose \( f(x) \), \( f'(x) \), \( g(x) \), and \( g'(x) \) have the values shown in the table:
| \( x \) | \(-7\) | \(-6\) | \(-5\) | \(-4\) | \(-3\) |
|----------|--------|--------|--------|--------|--------|
| \( f(x) \) | \(-9\) | \( 8 \) | \(-8\) | \(-6\) | \(8\) |
| \( f'(x) \) | \(-1\) | \(2\) | \(6\) | \(8\) | \(4\) |
| \( g(x) \) | \(10\) | \(-9\) | \(7\) | \(-6\) | \(-6\) |
| \( g'(x) \) | \(4\) | \(10\) | \(4\) | \(10\) | \(2\) |
**Find the following:**
1. \( (fg)'(-7) \)
2. \( \left(\frac{f}{g}\right)'(-7) \)
### Explanation of Functions and Derivatives
- \( f(x) \) and \( g(x) \) represent the values of two functions at specific points.
- \( f'(x) \) and \( g'(x) \) represent the values of the derivatives of these functions at the same points.
### Calculations:
1. **Finding \( (fg)'(-7) \)**
Using the Product Rule for derivatives:
\[ (fg)'(x) = f'(x)g(x) + g'(x)f(x) \]
Substitute \( x = -7 \):
\[ (fg)'(-7) = f'(-7)g(-7) + g'(-7)f(-7) \]
\[ (fg)'(-7) = (-1)(10) + (4)(-9) \]
\[ (fg)'(-7) = -10 - 36 \]
\[ (fg)'(-7) = -46 \]
2. **Finding \( \left( \frac{f}{g
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