Find the following using the table below. x f(x) g(x) g'(x) 14 74 23 3 1 2 4 3 4 3 h' (2) if h(x) = 3 4 2 1 2 دان 2 3 1 h' (2) if h(x) = f(x) · g(x) f(x) g(x)
Find the following using the table below. x f(x) g(x) g'(x) 14 74 23 3 1 2 4 3 4 3 h' (2) if h(x) = 3 4 2 1 2 دان 2 3 1 h' (2) if h(x) = f(x) · g(x) f(x) g(x)
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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![## Calculating Derivatives Using a Table
To solve the given problems, we use the following table of functions and their derivatives:
| \( x \) | \( 1 \) | \( 2 \) | \( 3 \) | \( 4 \) |
|---------|---------|---------|---------|---------|
| \( f(x) \) | \( 4 \) | \( 3 \) | \( 1 \) | \( 2 \) |
| \( f'(x) \) | \( 2 \) | \( 4 \) | \( 3 \) | \( 1 \) |
| \( g(x) \) | \( 1 \) | \( 4 \) | \( 3 \) | \( 2 \) |
| \( g'(x) \) | \( 4 \) | \( 2 \) | \( 3 \) | \( 1 \) |
### Problems
1. **Find \( h'(2) \) if \( h(x) = f(x) \cdot g(x) \)**
To find \( h'(x) \) when \( h(x) = f(x) \cdot g(x) \), use the product rule:
\[
h'(x) = f'(x) \cdot g(x) + f(x) \cdot g'(x)
\]
Substitute \( x = 2 \):
\[
h'(2) = f'(2) \cdot g(2) + f(2) \cdot g'(2)
\]
Using the table values:
\[
f'(2) = 4, \quad g(2) = 4, \quad f(2) = 3, \quad g'(2) = 2
\]
Hence:
\[
h'(2) = (4 \cdot 4) + (3 \cdot 2) = 16 + 6 = 22
\]
2. **Find \( h'(2) \) if \( h(x) = \frac{f(x)}{g(x)} \)**
To find \( h'(x) \) when \( h(x) = \frac{f(x)}{g(x)} \), use the quotient rule:
\[
h'(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95d4eca3-ae22-471e-b794-cce83c96d63b%2F23febcc1-805c-4477-a8dc-8a39c66a683d%2F4tldd3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Calculating Derivatives Using a Table
To solve the given problems, we use the following table of functions and their derivatives:
| \( x \) | \( 1 \) | \( 2 \) | \( 3 \) | \( 4 \) |
|---------|---------|---------|---------|---------|
| \( f(x) \) | \( 4 \) | \( 3 \) | \( 1 \) | \( 2 \) |
| \( f'(x) \) | \( 2 \) | \( 4 \) | \( 3 \) | \( 1 \) |
| \( g(x) \) | \( 1 \) | \( 4 \) | \( 3 \) | \( 2 \) |
| \( g'(x) \) | \( 4 \) | \( 2 \) | \( 3 \) | \( 1 \) |
### Problems
1. **Find \( h'(2) \) if \( h(x) = f(x) \cdot g(x) \)**
To find \( h'(x) \) when \( h(x) = f(x) \cdot g(x) \), use the product rule:
\[
h'(x) = f'(x) \cdot g(x) + f(x) \cdot g'(x)
\]
Substitute \( x = 2 \):
\[
h'(2) = f'(2) \cdot g(2) + f(2) \cdot g'(2)
\]
Using the table values:
\[
f'(2) = 4, \quad g(2) = 4, \quad f(2) = 3, \quad g'(2) = 2
\]
Hence:
\[
h'(2) = (4 \cdot 4) + (3 \cdot 2) = 16 + 6 = 22
\]
2. **Find \( h'(2) \) if \( h(x) = \frac{f(x)}{g(x)} \)**
To find \( h'(x) \) when \( h(x) = \frac{f(x)}{g(x)} \), use the quotient rule:
\[
h'(
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