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. 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. 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 Submit Question

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.
Chapter5: Graphs And The Derivative
Section5.CR: Chapter 5 Review
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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.
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.
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
Submit Question
Transcribed Image Text: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. 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. 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 Submit Question
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