3. (a) Use the table of data shown below to approximate the value of f'(2.5) x | 2 | 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 | 3 f(x) | 23 | 21 | 19.9 | 19 | 18.1 | 17.4 | 16.7 | 15.5 | 14.1 | 12 | 10 (b) Use your answer to part (a) to find the linearization of f(x) at the point x = 2.5
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5) using the given data. We can use the average rate of change between the points (2.4, 18.1) and (2.6, 16.7) to approximate the derivative at x = 2.5. f'(2.5) ≈ (f(2.6) - f(2.4)) / (2.6 - 2.4) = (16.7 - 18.1) / (2.6 - 2.4) = (-1.4) / 0.2 = -7 Now, we can find Show more…
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