run more smourhly and -. Assume that f and g are differentiable functions for which th known. O exponents, the calculations can O f(0) = 1, f(1) = 2, f(2)= 3, and f(3) = 0. f'(0) = 0, f'(1) = 2, f'(2) = 3, and f'(3) = 1. g(0) = 2, g(1) = 3, g(2) = 0, and g(3) = 1. O g' (0) = 1, g(1) = 0, g'(2) = 3, and g' (3) = 2. O leave A. Find (f + g)'(3) and (f - g)'(0). B. Find (fg)'(2) and (f/g)'(1). C. Find (f g)'(0) and (gof)(2). D. Find (2f - g²)'(3). O A) FL3) + 9¹3) 13) (f g)'(2)
run more smourhly and -. Assume that f and g are differentiable functions for which th known. O exponents, the calculations can O f(0) = 1, f(1) = 2, f(2)= 3, and f(3) = 0. f'(0) = 0, f'(1) = 2, f'(2) = 3, and f'(3) = 1. g(0) = 2, g(1) = 3, g(2) = 0, and g(3) = 1. O g' (0) = 1, g(1) = 0, g'(2) = 3, and g' (3) = 2. O leave A. Find (f + g)'(3) and (f - g)'(0). B. Find (fg)'(2) and (f/g)'(1). C. Find (f g)'(0) and (gof)(2). D. Find (2f - g²)'(3). O A) FL3) + 9¹3) 13) (f g)'(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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I need help with specifically C and D!!!
![### Differentiable Functions and Calculus Problems
**Problem 4:**
Assume that \( f \) and \( g \) are differentiable functions, for which the following values are known:
- \( f(0) = 1 \), \( f(1) = 2 \), \( f(2) = 3 \), and \( f(3) = 0 \).
- \( f'(0) = 0 \), \( f'(1) = 2 \), \( f'(2) = 3 \), and \( f'(3) = 1 \).
- \( g(0) = 1 \), \( g(1) = 3 \), \( g(2) = 0 \), and \( g(3) = 1 \).
- \( g'(0) = 1 \), \( g'(1) = 0 \), \( g'(2) = 3 \), and \( g'(3) = 2 \).
Tasks:
A. Find \((f + g)'(3)\) and \((f - g)'(0)\).
B. Find \((fg)'(2)\) and \((f/g)'(1)\).
C. Find \((f \circ g)'(0)\) and \((g \circ f)'(2)\).
D. Find \((2f - g^2)'(3)\).
**Solutions:**
**A.**
- \((f + g)'(3)\):
\[ f'(3) + g'(3) = 1 + 2 = 3 \]
- \((f - g)'(0)\):
\[ f'(0) - g'(0) = 0 - 1 = -1 \]
**B.**
- \((fg)'(2)\):
\[ (fg)'(x) = f(x) \cdot g'(x) + g(x) \cdot f'(x) \]
\[ (fg)'(2) = f(2) \cdot g'(2) + g(2) \cdot f'(2) \]
\[ = [3 \cdot 3] + [0 \cdot 3] = 9 + 0 = 9 \]
Diagrams and step-by-step calculations demonstrate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bb26d64-bb49-4ec5-afc7-ea9f4d31dfb0%2F4f6ba8ae-ab92-4111-ab4a-873ecee01e68%2F23abqcr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Differentiable Functions and Calculus Problems
**Problem 4:**
Assume that \( f \) and \( g \) are differentiable functions, for which the following values are known:
- \( f(0) = 1 \), \( f(1) = 2 \), \( f(2) = 3 \), and \( f(3) = 0 \).
- \( f'(0) = 0 \), \( f'(1) = 2 \), \( f'(2) = 3 \), and \( f'(3) = 1 \).
- \( g(0) = 1 \), \( g(1) = 3 \), \( g(2) = 0 \), and \( g(3) = 1 \).
- \( g'(0) = 1 \), \( g'(1) = 0 \), \( g'(2) = 3 \), and \( g'(3) = 2 \).
Tasks:
A. Find \((f + g)'(3)\) and \((f - g)'(0)\).
B. Find \((fg)'(2)\) and \((f/g)'(1)\).
C. Find \((f \circ g)'(0)\) and \((g \circ f)'(2)\).
D. Find \((2f - g^2)'(3)\).
**Solutions:**
**A.**
- \((f + g)'(3)\):
\[ f'(3) + g'(3) = 1 + 2 = 3 \]
- \((f - g)'(0)\):
\[ f'(0) - g'(0) = 0 - 1 = -1 \]
**B.**
- \((fg)'(2)\):
\[ (fg)'(x) = f(x) \cdot g'(x) + g(x) \cdot f'(x) \]
\[ (fg)'(2) = f(2) \cdot g'(2) + g(2) \cdot f'(2) \]
\[ = [3 \cdot 3] + [0 \cdot 3] = 9 + 0 = 9 \]
Diagrams and step-by-step calculations demonstrate
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