Find the difference quotient of f, that is, find [f(x + h) - f(x)]/h, where h cannot = 0, for the given function.
Be sure to simplify.
f(x) = (x+3)^2
NOTE: This question comes from a pre-calculus textbook and so the explanation must be in pre-calculus terms and NOT calculus.
The numerator in the difference quotient is . We substitute what we know:
The suggest that we should rearrange the first term in the numerator.
. Notice that the first term is just a binomial. Therefore we can take it's square as
The numerator becomes:
Notice the cancellation of the term:
The difference quotient is now:
The in the denominator cancels: