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4.3 Notes - c then c f can be classified as follows(1 If x...

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Calculus I Section 4.3 Increasing/Decreasing Functions and the First Derivative Test Test for Increasing and Decreasing Functions Let f be a continuous function on the closed interval [ a, b ] and differentiable on the open interval ( a, b ). 1. f is increasing if and only if _____________________________________________. 2. f is decreasing if and only if _____________________________________________. 3. f is constant if and only if _____________________________________________. Example: Determine where is increasing and decreasing. The First Derivative Test Let c be a critical number of a function f that is continuous on an open interval I containing c . If f is differentiable on the interval, except possibly at
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Unformatted text preview: c , then ) ( c f can be classified as follows. (1) If ) ( x f changes from negative to positive at c , then f(c) is a relative minimum of f . (2) If ) ( x f changes from positive to negative at c , then f(c) is a relative maximum of f . (3) If ) ( x f does not change sign at c , then f(c) is neither a relative minimum nor a relative maximum. Example: Locate all relative extrema for . For the following functions find all relative extrema and the intervals where the function is increasing and decreasing. Also, determine whether the graph of the function will have a smooth curve or a cusp at each relative extremum. , on the interval –...
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