For the function, find the following. (a) f'(x) 4 X 24 (b) f"(x) 3 x 6 (c) f"(x) 5,3 f(x) = 3 + 3x + - 1/2x² + 5x³ + 25x² + 120x5 6 24 + + 5x³ 5x² + 6 2 (d) f(4)(x) 5x² 2 2 x² +5x+5 2 +x+3 +5x+1
For the function, find the following. (a) f'(x) 4 X 24 (b) f"(x) 3 x 6 (c) f"(x) 5,3 f(x) = 3 + 3x + - 1/2x² + 5x³ + 25x² + 120x5 6 24 + + 5x³ 5x² + 6 2 (d) f(4)(x) 5x² 2 2 x² +5x+5 2 +x+3 +5x+1
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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![For the function, find the following derivatives:
Given:
\[ f(x) = 3 + 3x + \frac{1}{2}x^2 + \frac{5}{6}x^3 + \frac{5}{24}x^4 + \frac{1}{120}x^5 \]
(a) First Derivative, \( f'(x) \):
\[ f'(x) = \frac{x^4}{24} + \frac{5x^3}{6} + \frac{5x^2}{2} + x + 3 \]
(b) Second Derivative, \( f''(x) \):
\[ f''(x) = \frac{x^3}{6} + \frac{5x^2}{2} + 5x + 1 \]
(c) Third Derivative, \( f'''(x) \):
\[ f'''(x) = \frac{x^2}{2} + 5x + 5 \]
(d) Fourth Derivative, \( f^{(4)}(x) \):
The box for this derivative is empty, indicating it needs to be calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4f1bd45-0584-49f4-9d42-60805b104190%2Fcf67a8c9-dd3d-4be9-b9d0-6fc0bb3a9041%2F1jejoj_processed.png&w=3840&q=75)
Transcribed Image Text:For the function, find the following derivatives:
Given:
\[ f(x) = 3 + 3x + \frac{1}{2}x^2 + \frac{5}{6}x^3 + \frac{5}{24}x^4 + \frac{1}{120}x^5 \]
(a) First Derivative, \( f'(x) \):
\[ f'(x) = \frac{x^4}{24} + \frac{5x^3}{6} + \frac{5x^2}{2} + x + 3 \]
(b) Second Derivative, \( f''(x) \):
\[ f''(x) = \frac{x^3}{6} + \frac{5x^2}{2} + 5x + 1 \]
(c) Third Derivative, \( f'''(x) \):
\[ f'''(x) = \frac{x^2}{2} + 5x + 5 \]
(d) Fourth Derivative, \( f^{(4)}(x) \):
The box for this derivative is empty, indicating it needs to be calculated.
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