Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x³ - x² + x (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.) (-∞,1) U (1,∞) increasing decreasing DNE +x-8 (b) Find the relative extrema of f. relative maximum (x, y) = relative minimum (x, y) = concave downward (x, y) = (c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.) concave upward DNE DNE (d) Find the inflection points, if any, of f. X X X

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