Given f(x) = x^2 - 3x + 4, let's calculate the difference quotient:
\[F(x + \Delta x) - f(x) / \Delta x\]
Substitute the function values:
\[F(x + \Delta x) = (x + \Delta x)^2 - 3(x + \Delta x) + 4\]
\[f(x) = x^2 - 3x + 4\]
Now, substitute the values into the difference quotient and simplify:
\[\frac{(x + \Delta x)^2 - 3(x + \Delta x) + 4 - (x^2 - 3x + 4)}{\Delta x}\]
Simplify further:
\[\frac{x^2 + 2x\Delta x + \Delta x^2 - 3x - 3\Delta x + 4 - x^2 + 3x - 4}{\Delta x}\]
\[\frac{2x\Delta x + \Delta x^2 - 3\Delta x}{\Delta x}\]
\[2x + \Delta x - 3\]
As \(\Delta x\) approaches 0, the expression simplifies to \(2x - 3\).
So, the result is \(2x - 3\).