3. A table of values for the functions f(r) and f'(r) and a graph of the piecewise linear function g(x) are shown below. I| f(x)| f'(x) -1 11 -7 2 -2 -2 2 9 3 3 4 2 -1 3 -1 -2 g(x) (a) Given h(x) = f(x)g(x), find h'(1). f(r) find p'(2). g(1)' g(x) find q'(2). f(x)' (b) Given p(x) = (c) Given q(x) = f(x) g(r)' (d) Given q(x) = find q'(3). (e) Given €(x) = g(z) find l'(4).
3. A table of values for the functions f(r) and f'(r) and a graph of the piecewise linear function g(x) are shown below. I| f(x)| f'(x) -1 11 -7 2 -2 -2 2 9 3 3 4 2 -1 3 -1 -2 g(x) (a) Given h(x) = f(x)g(x), find h'(1). f(r) find p'(2). g(1)' g(x) find q'(2). f(x)' (b) Given p(x) = (c) Given q(x) = f(x) g(r)' (d) Given q(x) = find q'(3). (e) Given €(x) = g(z) find l'(4).
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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3.
![### Functions and Their Derivatives
**Table of Values:**
The table provides values for two functions \( f(x) \) and its derivative \( f'(x) \) at various points \( x \).
\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & f'(x) \\
\hline
-1 & 11 & -7 \\
0 & 2 & -2 \\
1 & -2 & 5 \\
2 & 9 & 3 \\
3 & 0 & 4 \\
4 & 1 & 2 \\
\hline
\end{array}
\]
**Graph Explanation:**
The graph illustrates the piecewise linear function \( g(x) \).
- The graph starts at \( (0, 3) \) and descends steeply to \( (1, -2) \).
- It remains constant from \( (1, -2) \) to \( (3, -2) \).
- It ascends steadily from \( (3, -2) \) to \( (5, 2) \).
**Problems:**
(a) Given \( h(x) = f(x)g(x) \), find \( h'(1) \).
(b) Given \( p(x) = \frac{f(x)}{g(x)} \), find \( p'(2) \).
(c) Given \( q(x) = \frac{g(x)}{f(x)} \), find \( q'(2) \).
(d) Given \( q(x) = \frac{f(x)}{g(x)} \), find \( q'(3) \).
(e) Given \( \ell(x) = \frac{g(x)}{\sqrt{x}} \), find \( \ell'(4) \).
Use calculus rules such as product rule, quotient rule, and chain rule along with the provided data to solve these problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F840f535b-f075-49f5-9fe8-c5a30f6f8dd7%2Fcbe41105-3d7a-4e6a-9f35-dc4152721168%2F0h1bez_processed.png&w=3840&q=75)
Transcribed Image Text:### Functions and Their Derivatives
**Table of Values:**
The table provides values for two functions \( f(x) \) and its derivative \( f'(x) \) at various points \( x \).
\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & f'(x) \\
\hline
-1 & 11 & -7 \\
0 & 2 & -2 \\
1 & -2 & 5 \\
2 & 9 & 3 \\
3 & 0 & 4 \\
4 & 1 & 2 \\
\hline
\end{array}
\]
**Graph Explanation:**
The graph illustrates the piecewise linear function \( g(x) \).
- The graph starts at \( (0, 3) \) and descends steeply to \( (1, -2) \).
- It remains constant from \( (1, -2) \) to \( (3, -2) \).
- It ascends steadily from \( (3, -2) \) to \( (5, 2) \).
**Problems:**
(a) Given \( h(x) = f(x)g(x) \), find \( h'(1) \).
(b) Given \( p(x) = \frac{f(x)}{g(x)} \), find \( p'(2) \).
(c) Given \( q(x) = \frac{g(x)}{f(x)} \), find \( q'(2) \).
(d) Given \( q(x) = \frac{f(x)}{g(x)} \), find \( q'(3) \).
(e) Given \( \ell(x) = \frac{g(x)}{\sqrt{x}} \), find \( \ell'(4) \).
Use calculus rules such as product rule, quotient rule, and chain rule along with the provided data to solve these problems.
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