Find the Difference Quotient of: (Please provide steps)
f(x)=x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1
You should know that the difference quotient is defined as:
$\displaystyle \frac{f(x+h)-f(x)}{h}$
So, utilize the binomial theorem, and if I were you I'd break the quotient up into pieces, then put it all back together at the end. You will be busy for a while.
Let us know if you get stuck...