Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the

Question

Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the inflection points.
f(x) = -x6 + 30x5 - 30x +3
For what interval(s) of x is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.)
B. The graph is never concave upward.
For what interval(s) of x is the graph of f concave downward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Type an exact answer. Use a comma to separate answers as needed.)
B. There are no inflection points.
(Type your answer in interval notation. Type an exact answer. Use
Determine the x coordinates of any inflection points of the graph of f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
separate answers needed.)
A. x=
B. The graph is never concave downward.

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