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Unformatted text preview: evaluate a derivative at a point where the function is not differentiable. Examples: ( 29 1/ , d x x x = returns& ( 29 ( 29 , d abs x x x = returns 1 3 → Graphing Derivatives Graph: ( 29 ln , y d x x = What does the graph look like? This looks like: 1 y x = Use your calculator to evaluate: ( 29 ln , d x x 1 x The derivative of is only defined for , even though the calculator graphs negative values of x . ln x x → There are two theorems on page 110: If f has a derivative at x = a , then f is continuous at x = a . Since a function must be continuous to have a derivative, if it has a derivative then it is continuous. → ( 29 1 2 f a x = ( 29 3 f b x = Intermediate Value Theorem for Derivatives Between a and b , must take on every value between and . f x 1 2 3 If a and b are any two points in an interval on which f is differentiable, then takes on every value between and . f x ( 29 f a x ( 29 f b x π...
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 Fall '05
 Riggs
 Derivative, Differential Calculus, Continuous function, Arches National Park, Hanford High School, Vickie Kelly

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