Respuesta :

8 is the difference quotient for the function f(x).

What is the difference quotient?

  • The average rate of change of the function over an interval is measured by the difference quotient (in this case, an interval of length h).
  • The instantaneous rate of change is hence the limit of the difference quotient (i.e., the derivative).

f(x ) =  x²

f(a) = a²

f(a+h) = ( a + h )²

f(a +h)-f(a)  =   ( a + h )² -  a²

                  =  a² + h² + 2ah - a²

                  =   h² + 2ah

now put a =  1 and h = 2

f(a +h)-f(a)  =   h² + 2ah

                  = 2² + 2 × 1 × 2

                  = 4 + 4  ⇒ 8

Learn more about difference quotient

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