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 notequal 0, for the following function. Be sure to simplify. F(x) = x^2 - 7x + 9 f(x + h)- f(x)/h=

Solution

f(x) = x^2 - 7x +9

f(x+h) = (x+h)^2 - 7(x+h) +9

= x^2 +h^2 +2hx -7x -7h +9

[f(x+h) - f(x)]/[ h]

= [ x^2 +h^2 +2hx -7x -7h +9 - (x^2 - 7x +9)]/h

= [ h^2 +2hx -7h]/h

= h +2x -7