The difference quotient For the function fx x2 3 construct

The difference quotient =

For the function ?f(x)= x^2 + 3?, construct and simplify the difference quotient f(x + h) - f(x)/h The difference quotient =

Solution

Given that

f(x) = x² + 3

f(x + h) = (x + h)² + 3

f(x + h) = x² + 2xh + h² + 3 [ since , (a + b)² = a² + 2ab + b² ]

Hence ,

f(x + h) - f(x) = x² + 2xh + h² + 3 - ( x² + 3)

= x² + 2xh + h² + 3 - x² - 3

  f(x + h) - f(x) = 2xh + h²

Therefore ,

   The difference quotient = [ f(x + h) - f(x) ] / h

= ( 2xh + h² ) / h

= h(2x + h)/h

The difference quotient = 2x + h