how do i find the difference quotient and simplify: f ( x ) = x 2 − x + 1 , f ( 2 + h ) − f ( 2 ) / h, h doesn't equal zero

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how do i find the difference quotient and simplify:  f  (  x  )  =      x    2    −  x  +  1  ,  f  (  2  +  h  )  −  f  (  2  )      /    h, h doesn&#039;t equal zero

Alden Holder · Accepted Answer

f  (  x  )  =      x          2        −  x  +  1            f      (      2      +      h      )      −      f      (      2      )        h    ,  h  ≠  0  ⇒            [      (      2      +      h              )                  2                    −      (      2      +      h      )      +      1      ]      −      [              2                  2                    −      2      +      1      ]        h    =            4      +      4      h      +              h                  2                    −      2      −      h      +      1      −      3        h    =                    h                  2                    +      3      h        h    =            h      (      h      +      3      )        h  =h+3

makaunawal5 · Accepted Answer

here all you have to do is plug in (2+h) in for all the x values in the       x    2    −  x  +  1 equation and (2) in forall the x values in the same equation and subtract the two. onceyou have done that divide it by h which cannot equal zero so your problem would look like this            (      (      2      +      h              )                  2                    −      (      2      +      h      )      +      1      )      −      (              2                  2                    −      2      +      1      )        h  from here just simplify            4      +      4      h      +              h                  2                    −      2      −      h      +      1      −      3        h  now just combine your like terms                    h                  2                    +      3      h        h  now factor out an h in the top            h      (      h      +      3      )        h  from here the h you just brought out will cancel out because of theh in the bottom so all that is left is (h+3)

how do i find the difference quotient and simplify: f(x) = x^2 - x + 1, f(2+h) - f(2)/ h, h doesn't equal zero

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