Find the difference quotient of f that is find fxhfxh h note

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) = -2x^2 + 4x - 3 f(x+h) - f(x)/h =

Solution

f(x) = -2x^2 +4x -3

f(x+h) = -2(x+h)^2 +4(x+h) -3

= -2(x^2 +h^2 +2xh) +4x +4h -3

= -2x^2 -2h^2 -4xh +4x +4h -3

Now, f(x+h) -f(x) = -2x^2 -2h^2 -4xh +4x +4h -3 - (- 2x^2 +4x -3)

= -2h^2 -4xh +4h

[ f(x+h) -f(x) ]/h = ( -2h^2 -4xh +4h)/h

= -2h -4x +4