For each of the following function, evaluate this expression f ( x + h ) − f ( x ) h 1. f ( x ) = x 2 − 4 x + 52. g ( x ) = x 3 − 2 x + 33. h ( x ) = 1 2 x

Question

For each of the following function, evaluate this expression            f      (      x      +      h      )      −      f      (      x      )        h  1.   f  (  x  )  =      x    2    −  4  x  +  52.   g  (  x  )  =      x    3    −  2  x  +  33.   h  (  x  )  =      1          2      x

akademiks1989rz · Accepted Answer

Step 11)             f      (      x      +      h      )      −      f      (      x      )        h    =            (      x      +      h              )        2            −      4      (      x      +      h      )      +      5      −      (              x        2            −      4      x      +      5      )        h    =                              ⧸                                      x          2                    +      2      x      h      +              h        2            −                        ⧸                            4        x            −      4      h      +                        ⧸                            5            −                        ⧸                                      x          2                    +                        ⧸                            4        x            −                        ⧸                            5              h    =            h      (      2      x      +      h      −      4      )        h    =  2  x  +  h  −  4Step 22)             g      (      x      +      h      )      −      g      (      x      )        h    =            (      x      +      h              )        3            −      2      (      x      +      h      )      +      3      −      (              x        3            −      2      x      +      3      )        h    =                    x        3            +      3              x        2            h      +      3      x              h        2            +              h        3            −      2      x      −      2      h      +      3      −              x        3            +      2      x      −      3        h    =            h      (      3              x        2            +      3      x      h      +              h        2            −      2      )        h    =  3      x    2    +  3  x  h  +      h    2    −  2Step 33)             h      (      x      +      h      )      −      h      (      x      )        h    =                    1                  2          (          x          +          h          )                    −              1                  2          x                      h    =            2      x      −      2      (      x      +      h      )              4      x      h      (      x      +      h      )        =            −      2      h              4      x      h      (      x      +      h      )        =            −      1              2      x      (      x      +      h      )

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