Let f(x) = k ln(x² + 3) + 5, where k < 0. Do the following. (a) Find the critical numbers of f, and make a sign chart for f'(x). (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. Justify each answer. (c) Find the value of x where f has a local extreme value, and classify this extrema as a local maximum or minimum. Justify your answer.

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