Suppose f (x) = ax 2 (x b)(x + c) 2 , where 0 < a

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Suppose f (x) = −ax2 (x − b)(x + c)2, where 0 < a < b < c.

(a) Graph f.

(b) In what interval(s) is there a local maximum value?

(c) Which numbers yield a local minimum value?

(d) Where is f (x) < 0?

(e) Where is f (−x − 4) < 0?

(f) Is f increasing, decreasing, or neither on (− ∞, −c ]?

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