Use a linear approximation (or differentials) to estimate the given number. (3.001)^3

Answer 1

f(x) = x³; f(3) = 3³ = 27; f'(x) = 3x²; f'(3) = 3·3² = 27;

L(x) = 27 + 27(x - 3); L(x) = 27x - 54;

(3.0001)³ ≈ L(3.001) = 27·3.001 - 54 = 27.027