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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4 Please show work thanks!
![**Question 4**
Let \( f(x) = 2 \log_8(x) \)
\( f'(x) = \) [Blank space for derivative]
\( f'(7) = \) [Blank space for numerical derivative evaluation]
**Explanation:**
This question involves finding the derivative \( f'(x) \) of the function \( f(x) \). The function given is \( f(x) = 2 \log_8(x) \), where the logarithm is base 8. The second part of the question requires evaluating the derivative at \( x = 7 \).
**Steps to Solve:**
1. **Find the Derivative \( f'(x) \):**
- Use the derivative rule for logarithms: \(\frac{d}{dx}[\log_b(x)] = \frac{1}{x \ln(b)}\).
- Apply the constant multiple rule: \(\frac{d}{dx}[a \cdot g(x)] = a \cdot g'(x)\).
2. **Evaluate \( f'(7) \):**
- Substitute \( x = 7 \) into the derivative function \( f'(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50c4a886-3e07-4312-95fc-3240a8ded880%2F102ec5a5-1c7f-4a7e-8ee0-e2053a36736e%2Fgj2opdq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 4**
Let \( f(x) = 2 \log_8(x) \)
\( f'(x) = \) [Blank space for derivative]
\( f'(7) = \) [Blank space for numerical derivative evaluation]
**Explanation:**
This question involves finding the derivative \( f'(x) \) of the function \( f(x) \). The function given is \( f(x) = 2 \log_8(x) \), where the logarithm is base 8. The second part of the question requires evaluating the derivative at \( x = 7 \).
**Steps to Solve:**
1. **Find the Derivative \( f'(x) \):**
- Use the derivative rule for logarithms: \(\frac{d}{dx}[\log_b(x)] = \frac{1}{x \ln(b)}\).
- Apply the constant multiple rule: \(\frac{d}{dx}[a \cdot g(x)] = a \cdot g'(x)\).
2. **Evaluate \( f'(7) \):**
- Substitute \( x = 7 \) into the derivative function \( f'(x) \).
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