3.3 How Derivatives Affect the Shape of a Graph

3.3 How Derivatives Affect the Shape of a Graph - Concavity...

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How Derivatives Affect the Shape of a Graph Section 3.3
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decreasing constant increasing
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Test for Increasing & Decreasing Functions
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Guidelines for Finding Intervals on Which a Function is Increasing or Decreasing
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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
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® When using the 1st 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.
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relative minimums relative maximums neither rel. max. or min.
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Defn:
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Unformatted text preview: Concavity Let f be differentiable on an open interval I . The graph of f is concave upward on I if f is increasing on the interval and concave downward on I if f is decreasing on the interval concave up concave down f is increasing f is decreasing Concavity Test Defn: Point of Inflection If the tangent line exists at a point which concavity changes, that point is an inflection point . point of inflection 2nd Derivative Test Joke Time What do clowns do after April 30th? Ma-trix What do you get when you add 50 female pigs and 50 male deer? $100,000 (100 sows an bucks)...
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3.3 How Derivatives Affect the Shape of a Graph - Concavity...

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