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Consider the function f(x) = 2x³ 3x² - 36x + 54. a. Find the first derivative. f'(x) = 6x² - 6x - 36 Incest b. List any critical values. (3,-27), (-2,98) This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. f"(x) = 12x - 6 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.

Consider the function f(x) = 2x³ 3x² - 36x + 54. a. Find the first derivative. f'(x) = 6x² - 6x - 36 Incest b. List any critical values. (3,-27), (-2,98) This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. f"(x) = 12x - 6 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.

Calculus For The Life Sciences
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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3.) questions c,d,f,g,h,i,j
Consider the function f(x) = 2x³ 3x² - 36x + 54. a. Find the first derivative. f'(x) = 6x² - 6x - 36 b. List any critical values. (3,-27), (-2,98) This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. 12x6 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.
Transcribed Image Text:Consider the function f(x) = 2x³ 3x² - 36x + 54. a. Find the first derivative. f'(x) = 6x² - 6x - 36 b. List any critical values. (3,-27), (-2,98) This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. This is not a decimal or integer value. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. 12x6 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.
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