Find the first derivative f' and the original function f. f"(x) = x³ – 18x, f' (1) = 0, ƒ(1) = 8 (Use symbolic notation and fractions where needed.) 35 f'(x) = 4 9x3 41 35x f(x) = %3D 20 3. 4 20
Find the first derivative f' and the original function f. f"(x) = x³ – 18x, f' (1) = 0, ƒ(1) = 8 (Use symbolic notation and fractions where needed.) 35 f'(x) = 4 9x3 41 35x f(x) = %3D 20 3. 4 20
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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f’x is correct, but the second one (f(x)), keeps showing its the wrong answer. I’m not sure what I did wrong. Thank you
![**Problem Statement:**
Find the first derivative \( f' \) and the original function \( f \).
Given:
\[ f'''(x) = x^3 - 18x \]
\[ f'(1) = 0 \]
\[ f(1) = 8 \]
(Use symbolic notation and fractions where needed.)
---
**Solution:**
1. **First Derivative:**
The first derivative \( f'(x) \) is:
\[
f'(x) = \frac{x^4}{4} - 9x^2 + \frac{35}{4}
\]
2. **Original Function:**
The original function \( f(x) \) is:
\[
f(x) = \frac{x^5}{20} - \frac{9x^3}{3} + \frac{35x}{4} + \frac{41}{20}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17dfd806-082f-4257-81d0-f087a7f9603f%2F34d216eb-3a2c-45de-88a6-ed05de0f30cb%2F61jeabn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the first derivative \( f' \) and the original function \( f \).
Given:
\[ f'''(x) = x^3 - 18x \]
\[ f'(1) = 0 \]
\[ f(1) = 8 \]
(Use symbolic notation and fractions where needed.)
---
**Solution:**
1. **First Derivative:**
The first derivative \( f'(x) \) is:
\[
f'(x) = \frac{x^4}{4} - 9x^2 + \frac{35}{4}
\]
2. **Original Function:**
The original function \( f(x) \) is:
\[
f(x) = \frac{x^5}{20} - \frac{9x^3}{3} + \frac{35x}{4} + \frac{41}{20}
\]
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