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
Test for Increasing & Decreasing Functions

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Guidelines for Finding Intervals on Which a Function is Increasing or Decreasing
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
® 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.
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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