**Problem** Evaluate the difference quotient for *f* (*x*) = *x*^{2} – 2*x* + 4.

This is a little different from but works the same way. Since a value is not supplied for *x*, we just leave it and work out the limit. Start by evaluating *f* (*x* + *h*):

Make sure you FOIL the square out and distribute the negative.

Now put this along with *f* (*x*) into the difference quotient.

As *h* gets smaller and smaller, the term in the middle gets smaller. This means the limit is equal to 2*x* – 2. Since the other terms do not contain *x*, they are unaffected when *h *gets small.