## anonymous 4 years ago Given the function f(x), the fraction f (x+h)-f(x)/h is the difference quotient associated with f. The determination of a function's difference quotient is the first step in determining the function's derivative and is an important topic in Calculus. For each of the following functions determine its difference quotient.

1. anonymous

$f (x)= \sqrt{x}$

2. anonymous

sqrt(x+h)-sqrt(x)/h => [(sqrt(x+h)-sqrt(x))*(sqrt(x+h)+sqrt(x)]/(h*(sqrt(x+h)+sqrt(x)) => (once cancelled) = h/(h*(sqrt(h+x)+sqrt(x))) = 1/(sqrt(x+h)+sqrt(x)) => (as h->0) = 1/2*sqrt(x) .. sorry this isn't typed up well computer is slow .. 1st part i rationalised the fraction btw. hope this helps

3. anonymous

4. anonymous