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.

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Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
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Consider the function f(x) 2x³6x² 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.
Transcribed Image Text:Consider the function f(x) 2x³6x² 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.
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