Find the first and second derivative at x = 2.5 of the following data | Numerical Methods 2082

Numerical Methods20825 marksNumerical: numerical differentiationDivided difference table for derivatives

Find the first and second derivative at $x = 2.5$ of the following data points.

$\begin{array}{|c|cccccc|}\hline x & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 \\ \hline f(x) & 2.375 & 4.5 & 7.625 & 12 & 17.875 & 23 \\ \hline \end{array}$

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Find the first and second derivative at $x = 2.5$ of the following data points.

$$\begin{array}{|c|cccccc|}\hline x & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 \ \hline f(x) & 2.375 & 4.5 & 7.625 & 12 & 17.875 & 23 \ \hline \end{array}$$

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$x$ 1.5 2.0 2.5 3.0 3.5 4.0 ----------------------------------- $f(x)$ 2.375 4.5 7.625 12 17.875 23 - Step size: $h = 0.5$ - Point of interest: $x = 2.5$ Take $x0 = 2.5$ so that $p = 0$ . First compute all differences carefully. $x$ $f$ $\Delta f$ $\Delta^2 f$ $\Delta^3 f$ $\Delta^4 f$

$x$ 1.5 2.0 2.5 3.0 3.5 4.0 ----------------------------------- $f(x)$ 2.375 4.5 7.625 12 17.875 23 - Step size: $h = 0.5$ - Point of interest: $x = 2.5$ Take $x0 = 2.5$ so that $p = 0$. First compute all differences carefully. $x$ $f$ $\Delta f$ $\Delta^2 f$ $\Delta^3 f$ $\Delta^4 f$

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Find the first and second derivative at x = 2.5 of the following data points.