'Relative minima' presentation slideshows

Chapter 3 Section 3.2

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Section 2.2 More on Functions and Their Graphs

Section 2.2 More on Functions and Their Graphs. Increasing and Decreasing Functions. The open intervals describing where functions increase, decrease, or are constant, use x-coordinates and not the y-coordinates. Use the graph to determine the intervals on which

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Graphing Using Derivatives

Graphing Using Derivatives. Step 1. find the 1 st derivative set it equal to zero solve it. f ( x ) = x 3 - 3 x 2. f '( x ) = 3 x 2 - 6 x = 3 x ( x -2) = 0 x = 0, x = 2 . Step 2. Making the 1 st derivative chart:

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Relative Extrema

Relative Extrema. Objective. To find the coordinates of the relative extrema of a function. Relative Extrema. Relative (local) extrema : points at which a function changes from increasing to decreasing, or from decreasing to increasing. Relative Extrema. Two Types of Relative Extrema

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NOTATION FOR HIGHER DERIVATIVES

NOTATION FOR HIGHER DERIVATIVES The second derivative of y = f ( x ) can be written using any of the following notations: f '' ( x ), The third derivative can be written in a similar way. For n ? 4, the nth derivative is written f ( n ) ( x ). SECOND DERIVATIVE TEST

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