Topic 6: Differentiation
             Jacques Text Book (edition 4 ):  
                         Chapter 4
            1.Rules of Differentiation 
            2.Applications 
                                                      1
         Differentiation is all about measuring 
                         change! 
        Measuring change in a linear function:
                     y = a + bx
      a= intercept
      b= constant slope i.e. the impact of a unit 
        change in x on the level of y
                                  y − y
              b=  ∆y        =       2     1
                     ∆x           x −x
                                    2     1
                                                     2
                       If the function is non-linear: 
                    40                                                2
                                          e.g. if y = x
                    30
                    20
                  y=x2
                    10
                     0
                       0123456
                      ∆y             y   − y               X
                           =  2 1 gives slope of the line
                      ∆x             x   − x
                                      2      1
                     connecting 2 points (x , y ) and (x ,y ) on a
                     curve                                    1     1               2   2
                        • (2,4) to (4,16): slope = (16-4)
                                                                            /(4-2) = 6 
                                                                    (36-4)
                        • (2,4) to (6,36): slope =                          /(6-2) = 8               3
             The slope of a curve is equal to the slope of 
              the line (or tangent) that touches the curve 
                                              at that point
                                                  Total Cost Curve
                   40
                   35
                   30
                   25
                  y=x220
                   15
                   10
                   5
                   0
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