The answer will be -2 - 2x.
Getting there will take a bit of algebra
Lim (h - > 0) (f (x + h) - f(x))/ h This is the definition, also know as the difference quotient.
To make things faster for me to type I am NOT going to continue to Lim (h --> 0).
Your instructor will mark you wrong if you do not continue to write it in.
(f(x +h) - f(x))/h =
(4 - 2(x +h) - (x + h)^2 - (4 - 2x - x^2)) / h = ((4 - 2x - 2h - x^2 - 2xh -h^2) - (4 - 2x - x^2))/h =
((4 - 2x - 2h -x^2 - 4xh - 2h^2 - 4 + 2x + x^2)/ h = (- 2h - 2xh - h^2) / h =
- 2 - 2x - h
Lim (h--> 0) - 2 - 2x - h = - 2 - 2x
Hope that helps
Getting there will take a bit of algebra
Lim (h - > 0) (f (x + h) - f(x))/ h This is the definition, also know as the difference quotient.
To make things faster for me to type I am NOT going to continue to Lim (h --> 0).
Your instructor will mark you wrong if you do not continue to write it in.
(f(x +h) - f(x))/h =
(4 - 2(x +h) - (x + h)^2 - (4 - 2x - x^2)) / h = ((4 - 2x - 2h - x^2 - 2xh -h^2) - (4 - 2x - x^2))/h =
((4 - 2x - 2h -x^2 - 4xh - 2h^2 - 4 + 2x + x^2)/ h = (- 2h - 2xh - h^2) / h =
- 2 - 2x - h
Lim (h--> 0) - 2 - 2x - h = - 2 - 2x
Hope that helps