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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]]

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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
  2. 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.)
    3. \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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