2007-09-12 No Derivative

# 2007-09-12 No Derivative - When Does a Function Not Have a...

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- . When Does a Function Not Have a Derivative at a Point? A function has a derivative at a point Xo if the slopes of the secant lines through P (xQ. f (xo» and a nearby point Q on the graph approach a limit as Q approaches P. Wheneve.fthe secants fail to take up a limiting position or become vertical as Q approaches P, the derivative does not e~ist. A function whosedgraph is otherwise smooth will fail to have a derivative at a point where the graph has
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Unformatted text preview: 1. a corner, where the one-sideal 2. a CllSP, where the slope of PQ derivatives differ . approaches 00 from one side and-00 from the other .11 _ 3. a vertical tangent, where the slope of PQ approaches 00 from both sides or approaches -00 from both sides (here, -(0) 4. a discontinuity. JUMp (t.JON-UMaIMle) 't1.SCo/J'n,J\JIN R61't\ cNA 8 I. . E 't)ISCONi)NVITY...
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• Fall '08
• Tyler/Ralston
• Derivative, Mathematical analysis, PQ approaches

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