f(x) = x? - 12x³ + 54x² - 108x + 81
a) Determine the intervals on which f(x) is concave
up and concave down.
f(x) is concave up on:
f(x) is concave down on:
b) Based on your answer to part (a), determine the
inflection points of f(x). Each point should be
entered as an ordered pair (that is, in the form (x, y)
).
(Separate multiple
answers by commas.)
c) Find the critical numbers of f(x) and use the
Second Derivative Test, when possible, to determine
the relative extrema. List only the \textit{x}-coordinates.
Relative maxima at:
(Separate
multiple answers by commas.)
Relative minima at:
(Separate
multiple answers by commas.)
Note: You can earn partial credit on this problem.