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:**
Find \( f'(x) \), \( f''(x) \), \( f'''(x) \), and \( f^{(4)}(x) \) for the function.
**Given Function:**
\[ f(x) = x^6 - 2x^5 + 4x - 4 \]
**Derivative Calculations:**
1. **First Derivative: \( f'(x) \)**
Apply the power rule to each term:
\[
f'(x) = 6x^5 - 10x^4 + 4
\]
2. **Second Derivative: \( f''(x) \)**
Differentiate \( f'(x) \):
\[
f''(x) = 30x^4 - 40x^3
\]
3. **Third Derivative: \( f'''(x) \)**
Differentiate \( f''(x) \):
\[
f'''(x) = 120x^3 - 120x^2
\]
4. **Fourth Derivative: \( f^{(4)}(x) \)**
Differentiate \( f'''(x) \):
\[
f^{(4)}(x) = 360x^2 - 240x
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Transcribed Image Text:**Problem Statement:**
Find \( f'(x) \), \( f''(x) \), \( f'''(x) \), and \( f^{(4)}(x) \) for the function.
**Given Function:**
\[ f(x) = x^6 - 2x^5 + 4x - 4 \]
**Derivative Calculations:**
1. **First Derivative: \( f'(x) \)**
Apply the power rule to each term:
\[
f'(x) = 6x^5 - 10x^4 + 4
\]
2. **Second Derivative: \( f''(x) \)**
Differentiate \( f'(x) \):
\[
f''(x) = 30x^4 - 40x^3
\]
3. **Third Derivative: \( f'''(x) \)**
Differentiate \( f''(x) \):
\[
f'''(x) = 120x^3 - 120x^2
\]
4. **Fourth Derivative: \( f^{(4)}(x) \)**
Differentiate \( f'''(x) \):
\[
f^{(4)}(x) = 360x^2 - 240x
\]
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