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Estimate \$f'\\!(\\var{x_0})\$ to one decimal place: [[0]]

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Estimate \$f''\\!(\\var{x_0})\$ to one decimal place: [[1]]

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Suppose I reveal that the function is a cubic, so that \$f(x) = a x^3 + b x^2 + c x + d\$. I will also tell you that \$\\{a,b,c,d\\} \\subset \\mathbb{Z}\$. Calculate the parameters \$a\$ to \$d\$.

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\$a = \$ [[0]]

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\$b = \$ [[1]]

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\$c = \$ [[2]]

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\$d = \$ [[3]]

I am thinking of a function, but I will not tell you what it is! But:

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1. It is at least twice-differentiable.
2. \n
3. I will tell you the value of the function anywhere you ask, to three decimal places. You can use the box below to inquire of me. (You may need to wait a little for it to load.)
4. \n
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{geogebra_applet('ufgKrAzb',defs)}

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Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.

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