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I'm reading Spivak's Calculus, there's a part where he suggests that the student should check some assertions:

$f(x)=x^2$

Then I've evaluated for $f(x+1)$ which is $f(x+1)=(x+1)^2=x^2+2x+1$. Why he says that $f(x+1)=f(x)+2x+1$? Does $f(x)=x^2$ in this case?

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    @Andrea Robert explained what I didn't know.2012-12-15

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Since $f(x)=x^2$, $f(x+1)=(x+1)^2=x^2+2x+1=f(x)+2x+1$ Both are correct

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    @BabakSorouh My assumption is that it's testing the algebra needed to set up $\frac{f(x+h)-f(x)}h$, and prepping the student to recognize the cancellation that will occur.2012-12-15