Derivative using definition: Problem 14 (1 point) For f(x)=6x^(2)+3x+4 fill in the following table at x=2 : [ egin{array}{|c|c|c|c|c|} hline x & f(x) & Delta x=x-2 & Delta f=f(x)-f(2) & frac{Delta f}{Delta x} \ hline 1.9 & 33.7 & -0.1 & 3.7 & -37 \ 1.99 & 39.67 & -0.01 & 9.67 & -967 \ 1.999 & 39.967 & -0.001 & 9.967 & -9967 \ 1.9999 & 39.9967 & -0.0001 & 9.9967 & -99967 \ 2.0001 & 40.0033 & 0.0001 & 10.0033 & 100033 \ 2.001 & 40.032 & 0.001 & 10.032 & 10032 \ 2.01 & 40.67 & 0.01 & 10.67 & 1067 \ 2.1 & 46.4 & 0.1 & 16.4 & 164 \ hline end{array} ] Use the table to estimate f'(2)=
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- We can see that as Δx approaches 0, the values for Δf/Δx are approaching a certain value. - We can estimate f'(2) by taking the average of these values. Show more…
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