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plotting - Getting the interpolation function from a list plot


I have conducted a chemistry experiment and obtained a list of concentrations of a reactant against time. I plot a graph of this using Mathematica's ListPlot functionality, as follows:


ListPlot[{{0, 0.562}, {10, 0.523}, {20, 0.480}, {30, 0.438}, {40, 0.398}, {50, 0.357},
 {60, 0.320}, {70, 0.285}, {80, 0.255}, {90, 0.230}, {100, 0.220}}, Joined -> True,
 InterpolationOrder -> 2, Mesh -> Full, AxesLabel -> {"Time (s)", "[A] (moldm^-3)"}]

This produces the graph below:


enter image description here



However, I wish to calculate the rate of reaction, for which I need the first derivative at $t=0$. I want to be able to get the interpolating function used by the ListPlot function when I specify InterpolationOrder -> 2, is this possible?


Thanks in advance!



Answer



Like Chris says:


data = {{0, 0.562}, {10, 0.523}, {20, 0.480}, {30, 0.438}, {40, 0.398}, {50, 0.357}, 
        {60, 0.320}, {70, 0.285}, {80, 0.255}, {90, 0.230}, {100, 0.220}}
f = Interpolation[data, InterpolationOrder -> 2]

then


f'[0]


returns



-0.0037

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