Answer:
-2x
Step-by-step explanation:
You want the "incremental quotient" for f(x) = -x² +6.
Incremental quotient
We assume you want the limit of the difference quotient:
[tex]\displaystyle\lim_{h\to0}{\dfrac{f(x+h)-f(x)}{h}}[/tex]
For the given definition of f(x), this is ...
[tex]\displaystyle\lim_{h\to0}{\dfrac{(-(x+h)^2+6)-(-x^2+6)}{h}}=\lim_{x\to0}{\dfrac{-2hx-h^2}{h}}=\boxed{-2x}[/tex]
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Additional comment
You can see that the quotient before the limit is taken is (-2x-h).
