Find the difference quotient of f that is find fx h fxh h

Find the difference quotient of f; that is, find f(x + h) - f(x)/h, h notequalto 0, for the following function. Be sure to simplify. f(x) = x^2 - 2x + 6 f(x + h) - f(x)/h = (Simplify your answer.)

Solution

f(x) = x^2 -2x +6

f(x+h) = (x+h)^2 - 2(x+h) +6

f(x+h) - f(x) = (x+h)^2 - 2(x+h) +6 - (x^2 -2x +6)

= h^2 +2hx   -2h

[ f(x+h) -f(x) ]/h = ( h^2 +2hx   -2h) /h = h +2x -2