Final answer:
To find the expression hf(x+h) - f(x) given a function f(x), we substitute the function into the expression and simplify step by step. The resulting expression is 4xh + 2h^2 - h.
Step-by-step explanation:
The given function is f(x) = 2x^2 - 3x on the interval [x, x+h]. To find the expression hf(x+h) - f(x), we substitute the given function into the expression.
hf(x+h) - f(x) = h(2(x+h)^2 - 3(x+h)) - (2x^2 - 3x)
Simplifying the expression step by step, we expand and combine like terms:
2hx^2 + 4hxh + 2hh^2 - 3hx - 3h - 2x^2 + 3x = 4hxh + 2hh^2 - h - 2x^2 + 3x
So, the correct answer is 4xh + 2h^2 - h.