Increasing and Decreasing Functions and the First Derivative

Increasing and Decreasing Functions and the First...

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Increasing and Decreasing Functions and the First Derivative Test Section 3.3
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decreasing constant increasing f ’ ’ (x) = 0 f ’ ’ (x) > 0 f ’ ’ (x) < 0
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Test for Increasing & Decreasing Functions If f ‘ (x) > 0 for all x in (a,b), then f is increasing on [a,b]. If f ‘ (x) < 0 for all x in (a,b), then f is decreasing on [a,b]. If f ‘ (x) = 0 for all x in (a,b), then f is constant on [a,b].
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Guidelines for Finding Intervals on Which a Function is Increasing or Decreasing Let f be continuous on (a,b) Find critical #s and use to determine test intervals. Determine the sign of f ‘ (x) at one test value in each of the intervals. Decide whether f is increasing or decreasing at each interval.( If f ‘ (x) + then increasing, if f ‘ (x < 0 then decreasing, If f ‘ (x) = 0 then constant.
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A function is strictly monotonic on an interval if it is either increasing on the entire interval or decreasing on the entire interval. monotonic not monotonic
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The First Derivative Test Let c be a critical number of a function
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Unformatted text preview: f that is continuous on an open interval I containing c . If f is differentiable on the interval, except possibly at c , then f(c) can be classified as follows: If f (x) changes from negative to positive at c , then f(c) is a relative minimum of f . If f (x) changes from positive to negative at c , then f(c) is a relative maximum of f . When using the 1 st Derivative Test, be sure to consider the domain of the function. The undefined points must be used with other critical #s to determine the test intervals. relative minimums relative maximums neither rel. max. or min. Joke Time What do clowns do after April 30 th ? Ma-trix What do you get when you add 50 female pigs and 50 male deer? $100,000 (100 sows an bucks) What do you call Calculus students who keep asking to go on a field trip to Cracker Barrel? Nothing. Theyre not going anywhere....
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Increasing and Decreasing Functions and the First...

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