Question 170000
Construct and simplify the difference quotient for f(x)= x^2-x.

-------------
Difference quotient: [f(x+h)-f(x)]/h
-------------
f(x+h) = (x+h)^2 - (x+h) = x^2+2hx+h^2-x-h
f(x) = x^2 - x
----------------------
Subtracting you get:
f(x+h)-f(x) = 2hx+h^2-h
----------------------
Dividing by h you get: 2x-1+h
----------------------
Cheers,
Stan H.