If f(x)= (1/2)x find the difference quotient and show work

Answer 1

f(x) = (1/2)x = x/2

f(x+h) = (x+h)/2

f(x+h)-f(x) = (x+h)/2 - x/2 = (x+h-x)/2 = h/2

[f(x+h)-f(x)]/h = (h/2)/h = 1/2

f'(x) = 1/2