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Unformatted text preview: x 2 x > 1 . 6? What do you note about continuity and dierentiability of f ( x ) at x = 1? Theorem: If f is dierentiable at x = a , then f is continuous at x = a . When is a function not dierentiable at a point? 6? 6? 6? Def. The graph of a function f ( x ) has a vertical tangent line at x = a if ex. Find f ( 1) if f ( x ) = ( x + 1) 1 = 3 . ex. Let f ( x ) = j x j . Use the limit denition to show that f ( x ) is not dierentiable at x = 0. ex. Let g ( x ) = x j x j . Show that g ( x ) is both continuous and dierentiable at x = 0. Higher Derivatives If y = f ( x ) is dierentiable, we can nd its derivative, a new function called f 00 ( x ). The limit denition: In the same way, the derivative of f 00 ( x ) is f 000 ( x ), and in general, we denote the n th derivative of f as f n ( x ). Other notation:...
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This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL

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