Answer:
The difference quotient and simplification will be = [4 -h-2x]
Step-by-step explanation:
The given equation is as follows: [tex]f(x) = 4x-x^2[/tex]
For finding the quotient and further simplification we must follow the following steps:
[tex][f(x+h) - f(x)] / h = [{4(x+h) -(x+h)^2} - 4x+x^2] / h[/tex]
What is simplification of algebraic operations?
Getting the functions in their lowest terms is known as simplification.
Brackets will get open and solved further;
[tex][f(x+h) - f(x)] / h = [4x+4h -x^2-h^2-2hx-4x+x^2) ] / h[/tex]
[tex][f(x+h) - f(x)] / h = [4h -h^2-2hx) ] / h[/tex]
Finally dividing the whole equation with h;
[tex]= [4 -h-2x][/tex]
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