Chap2_Sec8

# Chap2_Sec8 - THE DERIVATIVE AS A FUNCTION Example 1 (2.8)...

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The graph of a function f is given in the figure. Use it to sketch the graph of the derivative f’ . THE DERIVATIVE AS A FUNCTION Example 1 (2.8)

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For instance, for x = 5, we draw the tangent at P in the figure and estimate its slope to be about , so s This allows us to plot the point P’ (5, 1.5) on the graph of f’ directly beneath P . 3 2 '(5) 1.5 f THE DERIVATIVE AS A FUNCTION Example 1
Repeating this procedure at several points, we get the graph shown in this figure. THE DERIVATIVE AS A FUNCTION Example 1

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Notice that the tangents at A , B , and C are horizontal. s So, the derivative is 0 there and the graph of f’ crosses the x -axis at the points A’ , B’ , and C’ , directly beneath A , B , and C . THE DERIVATIVE AS A FUNCTION Example 1
A and B , the tangents have positive slope. s So, f’ ( x ) is positive there. Between B and C , and the tangents have negative slope. s

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## This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

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Chap2_Sec8 - THE DERIVATIVE AS A FUNCTION Example 1 (2.8)...

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