Find the difference quotient ,f(x+h-f(x)/h where, for the function below.
f(x)=-x^2+2x
Simplify your answer as much as possible.
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-2x + 2 - h

as h approaches 0 this approaches -2x + 2.

Step-by-step explanation:

Difference quotient:

=  -(x + h)^2 + 2(x + h)  - (-x^2 + 2x) / h

= - (x^2 + 2hx + h^2) + 2x + 2h + x^2 - 2x / h

= -x^2 - 2hx - h^2 + 2x + 2h + x^2 - 2x / h

=  (-2hx + 2h - h^2) / h

= -2x + 2 - h

As h approaches zero this approaches -2x + 2 which is the derivative of the function.

9

step-by-step explanation:

24 units

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