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How do I find the difference quotient? I already have the function of x and the equation and the restriction. How do I start?

Mathematics
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i have already plugged in (3+h) for x. what do i do next? @RadEn
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about derivative by using limit methods, right ?

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Other answers:

\(f(6)=5\) so we keep that number
then compute \[f(6+h)=5+6(6+h)-(6+h)^2\] to get \[5+36+6h-(36+12h+h^2)\] \[=5-6h-h^2\] then subtract 5 so that \(f(6+h)-f(6)=-6h-h^2\) divide by \(h\) and get \(-6-h\)
so i don't divide by H until i have plugged in both 6+h and 6 and simplified both? @satellite73
smart way : f(x) = 5+6x-x^2 f'(x) = 6-2x if u want find value of f'(6), u just plug in x=6 into f'(x) so, f'(6)=6-2(6)=6-12= ????????? but if u want using limit's method, like @satellite73 said
you do not divide by \(h\) until the end one reason is that you cannot divide by \(h\) until you have simplified the numerator so that everything without an \(h\) in it is gone
Thank you!! both of your answers were very helpful!
yw

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