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Unformatted text preview: maximum of f. If f '(x) < 0 for all x in (a, c) and f '(x) > 0 for all x in (c, b), then c is a local minimum of f. Example: Determine the intervals on which the function is increasing or decreasing and the local maximums and local minimums. Since the domain of f is the same as the domain of f', 4 is the only critical number of f. Testing: By the First Derivative Test, x = 4 is a local minimum. Example: Since the domain of f is the same as the domain of f', -3 and 6 are the only critical numbers of f. Testing: x < -3 f'(-10) = 672 f is increasing -3 < x < 6 f(0) = -108 f is decreasing x >6 f(10) = 312 f is increasing By the First Derivative Test, x = -3 is a local minimum and x = 6 is a local maximum. x < 4 f'(0) = -8 f is decreasing x > 4 f'(5) = 2 f is increasing...
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