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Use linear approximation to estimate f(3.9) given that f(4) = 3 and f'(4) = 6. (Simplify your answer.)

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Final answer:

To estimate f(3.9) using linear approximation, substitute the given values into the formula and simplify the expression.

Step-by-step explanation:

To estimate f(3.9) using linear approximation, we can use the formula:

f(3.9) ≈ f(4) + f'(4)(3.9 - 4)

Given that f(4) = 3 and f'(4) = 6, we can substitute these values into the formula:

f(3.9) ≈ 3 + 6(3.9 - 4)

Simplifying the expression:

f(3.9) ≈ 3 - 6(0.1) = 3 - 0.6 = 2.4

Therefore, f(3.9) ≈ 2.4.

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