Pre Calculus Simply

Question

f ( x + h) − f (x) / h ,where h≠0 and f (x ) = 2/x

Answer 1

f(x) =2/x

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

f(x+h)-f(x) = 2/(x+h) - 2/h = (2h - 2x-2h)/ch(hx+x^2) = -2h(hx+x^2)

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

check the answer by comparing it with the f'(x) =

derivative of (2/x)' = (2x^-1)' = -2/x^2 which = the difference quotient when h=0