Consider the function f(x) = 2x3 - 6x² - 18x + 54. a. Find the first derivative. f'(x) b. List any critical values. c. Identify intervals of increase.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
icon
Related questions
Question
Question 1
Textbook
Videos
<
>
Consider the function f(x) = 2x³ - 6x² - 18x + 54.
Submit Question
M MyOpenMath
a. Find the first derivative. f'(x) =
b. List any critical values.
c. Identify intervals of increase.
d. Identify intervals of decrease.
e. Find the second derivaitve. f''(x) =
f. Use parts b through e to identify maximums as points.
g. Use parts b through e to identify minimumns as points.
h. Use the second derivative to identify intervals where f(x) is concave up.
i. Use the second derivative to identify intervals where f(x) is concave down.
Jump to Answer
j. Use the second derivative to find any inflection points.
k. Upload a sketch of the function based on the information above and the intercepts.
Choose File No file chosen
M MyO
Transcribed Image Text:Question 1 Textbook Videos < > Consider the function f(x) = 2x³ - 6x² - 18x + 54. Submit Question M MyOpenMath a. Find the first derivative. f'(x) = b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. f''(x) = f. Use parts b through e to identify maximums as points. g. Use parts b through e to identify minimumns as points. h. Use the second derivative to identify intervals where f(x) is concave up. i. Use the second derivative to identify intervals where f(x) is concave down. Jump to Answer j. Use the second derivative to find any inflection points. k. Upload a sketch of the function based on the information above and the intercepts. Choose File No file chosen M MyO
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning