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Let f be a differentiable function with f(8) = -5 and f'(8) = 3. What is the value of the approximation of...

Let f be a differentiable function with f(8) = -5 and f'(8) = 3.
What is the value of the approximation of f(8.1) using the function's local linear approximation at x = 8?
Choose 1 answer:
A. -4.8
B. -4.7
C. -4.6
D. -4.5

Answer

To approximate f(8.1) using the local linear approximation, we use the formula:

f(8.1) ≈ f(8) + f'(8) * (8.1 - 8)

Substitute the given values:

f(8.1) ≈ -5 + 3 * (8.1 - 8)

f(8.1) ≈ -5 + 3 * 0.1

f(8.1) ≈ -5 + 0.3

f(8.1) ≈ -4.7

Answer: B. -4.7

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