A. For the interval from 5 to 5.1, we have:
$$f'(5) \approx \frac{f(5.1) - f(5)}{5.1 - 5}$$
Now, we need to find the values of $f(5)$ and $f(5.1)$:
$$f(5) = 3(5)^2 - 5 + 2 = 72$$
$$f(5.1) = 3(5.1)^2 - 5.1 + 2 \approx 78.31$$
So, the estimate of $f'(5)$ using
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