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Math150Ch3Review - MATH 150 CHAPTER 3 REVIEW SECTION 3.1...

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MATH 150 - CHAPTER 3 REVIEW SECTION 3.1: INTRODUCTION Secant lines (related to the graph of y f x = ( ) ) slope = average rate of change of with respect to on or = or y x a a h a b f a h f a h f b f a b a , , + [ ] [ ] + ( ) - ( ) ( ) - ( ) - If this h f a ª ª ¢ ( ) 0, , if it exists. Tangent lines slope = instantaneous rate of change of with respect to at = if it exists. Use algebra to work through this! = You may use our shortcuts unless you re told to use the limit definition. y x a f a h f a h f a h lim Æ + ( ) - ( ) ¢ ( ) ¢ ( ) 0 Slopes and equations of tangent lines Rectilinear motion Velocity = [Instantaneous] rate of change of position with respect to time. v t s t ( ) = ¢ ( ) SECTION 3.2: ¢ ( ) f x Limit definition of the derivative ¢ ( ) + ( ) - ( ) Æ f x f x h f x h h = if it exists. Use algebra to work through this! lim 0 Key cases when the derivative is “DNE” Where there is a… m m L R = left - hand derivative; = right - hand derivative ( ) 1) Discontinuity 2) Corner m m L R π (Maybe one is ±• , but not both.) 3) Vertical tangent line m L is or -• , and m R is or -• .
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