Final answer:
The difference quotient for the function f(x) = 3x - x^2 is 3 - 2x - h.
Step-by-step explanation:
The difference quotient for the function f(x) = 3x - x^2 can be evaluated using the formula (f(x+h) - f(x))/h.
Substituting the given function into the formula, we have:
((3(x+h) - (x+h)^2) - (3x - x^2))/h
Simplifying this expression, we get:
(3x + 3h - (x^2 + 2xh + h^2) - 3x + x^2)/h
Combining like terms, we can cancel out the 3x and x^2 terms, resulting in:
(3h - 2xh - h^2)/h
Factoring out an h from the numerator:
(h(3 - 2x - h))/h
Cancelling out the h terms, we are left with:
3 - 2x - h
Therefore, the difference quotient for the function f(x) = 3x - x^2 is 3 - 2x - h.