18x + 54. 6x² - 12x - 18 a. Find the first derivative. f'(x) = b. List any critical values. -1,3 c. Identify intervals of increase. (-∞0,-1)U(3,00) d. Identify intervals of decrease. (-1,3) e. Find the second derivaitve. f''(x) = 12x12 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

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
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Consider the function f(x) = 2x³ 6x² 18x + 54.
a. Find the first derivative. f'(x) = 6x² - 12x - 18
b. List any critical values. -1,3
c. Identify intervals of increase. (-∞0,-1)U(3,00)
d. Identify intervals of decrease. (-1,3)
e. Find the second derivaitve. f''(x) = 12x - 12
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) = 6x² - 12x - 18 b. List any critical values. -1,3 c. Identify intervals of increase. (-∞0,-1)U(3,00) d. Identify intervals of decrease. (-1,3) e. Find the second derivaitve. f''(x) = 12x - 12 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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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,