Which of the following corresponds to the derivative of f(x)=1x+2 at x = 2, using the alternate definition of a derivative, reduced to its simplest form before taking the limit?

Answer 1

The alternate definition of a derivative states that the derivative of a function f(x) at a point x = x0 is given by the limit as h approaches 0 of (f(x0 + h) - f(x0))/h.

Applying this definition to the function f(x) = 1x + 2 at x = 2, we substitute x0 = 2:
(f(2 + h) - f(2))/h
[(1(2 + h) + 2) - (1(2) + 2)]/h
[(2 + h + 2) - (2 + 2)]/h
[(4 + h) - 4]/h
(4 + h - 4)/h
h/h
1

Therefore, the derivative of f(x) = 1x + 2 at x = 2, using the alternate definition, reduced to its simplest form before taking the limit, is 1.