Explanation:
We know that f(x) = - x² + x - 6
Then, we can find f(x + h) as follows:
f(x + h) = -(x + h)² + (x + h) - 6
f(x + h) = -(x² + 2xh + h²) + x + h - 6
f(x + h) = -x² - 2xh - h² + x + h - 6
Then, we can find the difference quotient as
[tex]\frac{f(x+h)-f(x)}{h}=\frac{(-x^2-2xh-h^2+x+h-6)-(-x^2+x-6)_{}}{h}[/tex]
Simplifying, we get:
[tex]\begin{gathered} =\frac{-x^2-2xh-h^2+x+h-6+x^2-x+6}{h} \\ =\frac{-2xh-h^2+h}{h} \\ =-2x-h+1 \end{gathered}[/tex]
Therefore, the answer is
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