In Exercises 5-8, use the definition f'(a) = lim x→a f(x) = f(a) to find the derivative of the given function at the given value of a. 6. f(x) = x² + 4, a = 1 8. f(x) = 2x + 3, a = = −1 = 1/x, a = 7. f(x) = √x + 1, a = 3 9. Find f(x) if f(x)= 3x - 12. 10. Find dy/dx if v = 7 2 x - a
In Exercises 5-8, use the definition f'(a) = lim x→a f(x) = f(a) to find the derivative of the given function at the given value of a. 6. f(x) = x² + 4, a = 1 8. f(x) = 2x + 3, a = = −1 = 1/x, a = 7. f(x) = √x + 1, a = 3 9. Find f(x) if f(x)= 3x - 12. 10. Find dy/dx if v = 7 2 x - a
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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![In Exercises 5–8, use the definition
\[ f'(a) = \lim_{{x \to a}} \frac{f(x) - f(a)}{x - a} \]
to find the derivative of the given function at the given value of \( a \).
1. **Exercise 5:**
\[
f(x) = \frac{1}{x}, \quad a = 2
\]
2. **Exercise 6:**
\[
f(x) = x^2 + 4, \quad a = 1
\]
3. **Exercise 7:**
\[
f(x) = \sqrt{x} + 1, \quad a = 3
\]
4. **Exercise 8:**
\[
f(x) = 2x + 3, \quad a = -1
\]
5. **Exercise 9:**
Find \( f'(x) \) if \( f(x) = 3x - 12 \).
6. **Exercise 10:**
Find \( \frac{dy}{dx} \) if \( y = 7x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e635601-9da2-4fe2-987c-7194620410e8%2Faa8b7cf5-343f-41e2-9af2-c7245de8a31f%2F7w0sgra_processed.png&w=3840&q=75)
Transcribed Image Text:In Exercises 5–8, use the definition
\[ f'(a) = \lim_{{x \to a}} \frac{f(x) - f(a)}{x - a} \]
to find the derivative of the given function at the given value of \( a \).
1. **Exercise 5:**
\[
f(x) = \frac{1}{x}, \quad a = 2
\]
2. **Exercise 6:**
\[
f(x) = x^2 + 4, \quad a = 1
\]
3. **Exercise 7:**
\[
f(x) = \sqrt{x} + 1, \quad a = 3
\]
4. **Exercise 8:**
\[
f(x) = 2x + 3, \quad a = -1
\]
5. **Exercise 9:**
Find \( f'(x) \) if \( f(x) = 3x - 12 \).
6. **Exercise 10:**
Find \( \frac{dy}{dx} \) if \( y = 7x \).
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