This table gives select values of the differentiable function f. x | 0 | 3 | 5 | 6 | 9 f(x) | 72 | 95 | 112...

Question

This table gives select values of the differentiable function f.
x | 0 | 3 | 5 | 6 | 9
f(x) | 72 | 95 | 112 | 77 | 54
What is the best estimate for f'(4) we can make based on this table?
Choose 1 answer:
A) -2
B) 8.5
C) 103.5
D) 17

SnapAndSolve AI · Accepted Answer

To estimate f'(4), we can use the average rate of change between the points closest to x = 4. These points are x = 3 and x = 5.

The average rate of change is given by:

f'(4) ≈ (f(5) - f(3)) / (5 - 3)

Substitute the given values:

f'(4) ≈ (112 - 95) / (5 - 3) = 17 / 2 = 8.5

Therefore, the best estimate for f'(4) is B) 8.5.

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This table gives select values of the differentiable function f. x | 0 | 3 | 5 | 6 | 9 f(x) | 72 | 95 | 112...

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