Find the average rate of change of f ( x ) = x 2 + 3 x − 2 , x = a , x = a + h

Question

Find the average rate of change of   f  (  x  )  =      x    2    +  3  x  −  2  ,     x  =  a  ,     x  =  a  +  h

Maleah Lester · Accepted Answer

f  (  x  )  =      x    2    +  3  x  −  2    f  (  a  +  h  )  =  (  a  +  h      )    2    +  3  (  a  +  h  )  −  2    =      a    2    +  2  a  h  +      h    2    +  3  a  +  3  h  −  2    f  (  a  )  =      a    2    +  3  a  −  2Average rate   =            f      (      a      +      h      )      −      f      (      a      )              a      +      h      −      a          =                    a        2            +      2      a      h      +              h        2            +      3      a      +      3      h      −      2      −              a        2            −      3      a      +      2        h      =            2      a      h      +              h        2            +      3      h        h      =            h      (      h      +      2      a      +      3      )        h      =  h  +  2  a  +  3

Find the average rate of change of f(x)= x^2+3x-2; x=a, x= a+h

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