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.