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Efficient Plotting of Polynomials

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johnbchron:
f (x + 1) = 3 + 2(x + 1) - 3(x + 1)2 + (x + 1)3
f (x + 1) = 3 + 2x + 2 - 3(x2 + 2x + 1) + (x3 + 2x2 + x + x2 + 2x + 1)
f (x + 1) = (x3) + (-3x2 + 2x2 + x2) + (2x - 6x + x + 2x) + (3 + 2 - 3 + 1)
f (x + 1) = x3 - x + 3


it leaves -x, which + 3x = 2x.

I could be completely misunderstanding this though...

Xeda112358:
Your computation of f(x+1) is correct, but then you need to subtract f(x), so:
##
\begin{aligned}
f(x+1)-f(x)&=(x^{3}-x+3)-(x^{3}-3x^{2}+2x+3),\\
&=x^{3}-x+3-x^{3}+3x^{2}-2x-3,\\
&=-3x+3x^{2},\\
&=3x^{2}-3x.\\
\end{aligned}
##MathJax.Hub.Queue(["Typeset", MathJax.Hub, document.getElementById("bbclatex66487fbc8ad5a")]);console.log("Queued!");

johnbchron:
Ah yes, I see now

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