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SurCalCh2Sec7 - tangent line is vertical This is also a...

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2.7 – Nondifferentiable Functions TV Spring 2001 A function is said to be nondifferentiable at if the derivative does not exist at that x value. c x = Causes of nondifferentiability (from a graphical perspective) Discontinuities—If the graph is discontinuous at a particular x-value then it cannot have a tangent line there. If it cannot have a tangent line there, it has no derivative there. Vertical Tangent—The slope of a vertical line is undefined, therefore the derivative is undefined at any x-value where the
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Unformatted text preview: tangent line is vertical. This is also a point of nondifferentiability. Corner Points—If the graph has a corner at x=c the derivative as and the derivative as disagree. In other words, there is not a well-defined tangent line at that x value. This is also an x-value where the graph is nondifferentiable. + → h − → h Examples:...
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