2.1 The Derivative

# 2.1 The Derivative - 2.1THEDERIVATIVE

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2.1 THE DERIVATIVE For a linear function, f(x) = mx + b, the average rate of change is equal to the slope of the line.   For non-linear   functions, the rate of change at x = c is given by the slope of the tangent line at P(c, f(c)).  Average rate of change of   f(x) as x varies from x = c to x = h+c is given by the ratio  rate ave  =  in f( ) ( ) ( ) ( ) ( ) ( ) change x f c h f c f c h f c change in x c h c h + - + - = = + - . This expression  is called the difference quotient.  The derivative of a function is the limit of the difference quotient as h   0:  f’(x) =  h x f h x f h ) ( ) ( lim 0 - + .  The process of computing the derivative is called differentiation and f(x) is differentiable at  x = c  if  f’(c)  exists.  The  slope of the tangent line  to the curve  y = f(x)  at the point (c, f(c)) is  m tan  = f’(c) .  To find the equation

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## This note was uploaded on 01/04/2012 for the course MAC 2233 taught by Professor Royer during the Fall '08 term at FIU.

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2.1 The Derivative - 2.1THEDERIVATIVE

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