Answer the following questions for the function f(x) = - 8x°- 36x +240x - 11. a. Find formulas for f'(x) and f'"(x). f'(x) = - 24x -72x + 240 f"(x) = 48x - 72 Enter f(x), f'(x), and f'"(x) into your grapher to examine the table. b. The formula for the first derivative f'(x) can be factored. Set f'(x) = 0 to find the two critical numbers. Hint You can factor out - 24 from all terms in the formula for f'(x). You can also scroll the table function on your calculator. The critical values are x= 2,-5. (Use a comma to separate answers as needed ) c. Use your table to complete the following. At the negative critical value listed in part b, what does your table tell you about the value of the second derivative? f"O=(Type integers or simplified fractions.)
Answer the following questions for the function f(x) = - 8x°- 36x +240x - 11. a. Find formulas for f'(x) and f'"(x). f'(x) = - 24x -72x + 240 f"(x) = 48x - 72 Enter f(x), f'(x), and f'"(x) into your grapher to examine the table. b. The formula for the first derivative f'(x) can be factored. Set f'(x) = 0 to find the two critical numbers. Hint You can factor out - 24 from all terms in the formula for f'(x). You can also scroll the table function on your calculator. The critical values are x= 2,-5. (Use a comma to separate answers as needed ) c. Use your table to complete the following. At the negative critical value listed in part b, what does your table tell you about the value of the second derivative? f"O=(Type integers or simplified fractions.)
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...
Related questions
Question
9
Transcribed Image Text:Answer the following questions for the function f(x) = - 8x° – 36x² + 240x – 11.
a. Find formulas for f'(x) and f''(x).
f'(x) = - 24x– 72x + 240
f''(x) =
48x - 72
Enter f(x), f'(x), and f'"(x) into your grapher to examine the table.
b. The formula for the first derivative f'(x) can be factored. Set f'(x) = 0 to find the two critical numbers. Hint. You can factor out – 24 from all terms in the formula for
f'(x). You can also scroll the table function on your calculator.
The critical values are x= 2,- 5. (Use a comma to separate answers as needed )
c. Use your table to complete the following.
At the negative critical value listed in part b, what does your table tell you about the value of the second derivative?
f"(D =(Type integers or simplified fractions )
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning