Given the following table of values of f(x)=logxf(x) = \log xf(x)=logx, what…
2021
Given the following table of values of f(x)=logxf(x) = \log xf(x)=logx, what is the value of f′(3)?
- A.
0.125
- B.
0.225
- C.
0.208
- D.
0.278
Attempted by 1 students.
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Correct answer: A
If the function is f(x) = ln(x) (natural log):
The derivative f'(x) = 1/x.
At x = 3, f'(3) = 1/3 is approximately 0.333.
If the function is f(x) = log10(x) (common log):
The derivative f'(x) = 1 / (x * ln(10)).
Using ln(10) is approximately 2.303:
f'(3) = 1 / (3 * 2.303) = 1 / 6.909 is approximately 0.1447, which is approximately 0.145.
Note: Since none of the provided options (0.125, 0.225, 0.208, 0.278) match the analytical results exactly, please ensure the table values were used for a numerical derivative approximation (e.g., (f(3+h) - f(3-h)) / 2h).