Using derivatives, it is found that the best estimate of f '(2) based on this table of values is of 10.
The rate of change from x = 0 to x = 2 is given by:
[tex]r_1 = \frac{2 - (-16)}{2 - 0} = \frac{18}{2} = 9[/tex]
From x = 2 to x = 4, it is given by:
[tex]r_2 = \frac{24 - 2}{4 - 2} = \frac{22}{2} = 11[/tex]
The average of these rates is:
[tex]A = \frac{r_1 + r_2}{2} = \frac{9 + 11}{2} = 10[/tex]
Hence, the best estimate of f '(2) based on this table of values is of 10.
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