Help me with calculus

Question

Use an appropriate local linear approximation to estimate the value of the given quantity (1.97)³

Answer 1

f(x) = x³; f(2) =2³ = 8; f'(x) = 3x²; f'(2) = 12;

Now linear approximation L(x) = 8 +12(x - 2); L(x) = 12x - 16

1.97³ = f(1.97) ≈ L(1.97) = 12·1.97 - 16 = 7.64