Answer:
2x + 2 + h.
Explanation:
F(x+h) is f(x) where x+h replaces x:-
f(x + h) = (x + h)^2 + 2(x + h) - 3
[f(x+h) - f(x)] / h
= (x + h)^2 + 2(x + h) - 3 - (x^2 + 2x - 3) / h
= [x^2 + 2hx + h^2 + 2x + 2h - 3 - x^2 - 2x + 3] / h
= (2hx + h^2 + 2h) / h
= 2x + 2 + h
The limit of [f(x+h) - f(x)] / h as h ----> 0 is 2x + 2.
We refer to 2x + 2 as the derivative of x^2 + 2x - 3.