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 - 3x + 7 f(x + h) - f(x)/h = (Simplify your answer.)

Solution

f(x) = x^2 -3x + 7

f(x+h) = (x+h)^2 - 3(x+h) + 7 = x^2 +2xh +h^2 -3x-3h+7

{ f(x+h) - f(x) } / h

plugging the values

{ x^2 +2xh +h^2 -3x-3h+7 - x^2 +3x - 7 } / h = { 2xh + h^2 - 3h } / h

= 2x + h - 3

or h + 2x - 3