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I came across this question:

Suppose $f(x)=x^3-x+\frac{1}{4}$, What's the value of $f [0,0.1,0.2,0.3,0.4]$?

The problem is, I have no idea what is being asked, I'm unfamiliar with the notation "$f[0,0.1,0.2,0.3,0.4]$".

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    I'd agree with user12477's suggestion about context. Sensible people don't just start using weird notation without first explaining it.2012-02-14
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    @GerryMyerson: I have a bunch of questions without context, otherwise I wouldn't ask here.2012-02-14
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    @Gigili: what Gerry is telling you here is that you should have mentioned the book/paper/whatever where you saw this notation. This is explicitly requested in the popup for the [tag:notation] tag, among other things.2012-02-14

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This notation is used for divided differences, so perhaps that is what you are being asked to calculate. Giving a context for the question would help: divided differences arise in polynomial interpolation.

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    ...and since the underlying function is a cubic polynomial, while the divided difference sought is supposed to be the coefficient for a quartic interpolating polynomial, then... :)2012-02-14
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    Thank you, that was it. I'm trying to solve the problem now.2012-02-14
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    @J.M.: I didn't get your point, would you elaborate? I'd guess there's a point or hint, otherwise the computation is so long. Is it equal to zero?2012-02-14
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    @Gigili: Interpolation polynomials in Newton form go something like $d_0 + (x-x_1)(d_1 +(x-x_2)(d_2+\cdots))$. An $n$-th order polynomial is supposed to only have $n+1$ of those $d_k$'s (in much the same way that it can only have $n+1$ coefficients), so...2012-02-14
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    @J.M.: Got it, thank you. Should I post an answer to my question or what user12477 posted is enough?2012-02-14
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    @Gigili: entirely your call. But I deliberately left gaps in reasoning in my comment that you have to fill, should you decide to post an answer.2012-02-14
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As user12477 pointed out, it's Newton's divided differences interpolation polynomial and as J.M. pointed out, while $f(x)$ is a cubic function (polynomial of degree $n=3$), the divided difference on $n+1=4$ points (more than $n$ points generally) is equal to zero.