Use the given function and the given interval to complete parts a and b.
$f(x) = -2x^3 + 18x^2 - 30x$ on $[0,6]$
a. Determine the absolute extreme values of f on the given interval when they exist.
b. Use a graphing utility to confirm your conclusions.
a. What is/are the absolute maximum/maxima of f on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The absolute maximum/maxima is/are $\Box$ at $x = \Box$.
(Use a comma to separate answers as needed. Type exact answers, using radicals as needed.)
B. There is no absolute maximum of f on the given interval.
What is/are the absolute minimum/minima of f on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The absolute minimum/minima is/are $\Box$ at $x = \Box$.
(Use a comma to separate answers as needed. Type exact answers, using radicals as needed.)
B. There is no absolute minimum of f on the given interval.
b. Choose the correct answer below.
A.
[Graph A]
B.
[Graph B]
C.
[Graph C]
D.
[Graph D]
