An economist had determined that a certain country’s gross domestic product (GDP) is approximated by the function f (x) = 540x1/3

Question

f(x) is measured in billions of dollars and x is the capital outlay in billions of dollars. Use differentials to estimate the change in country’s GDP if the country’s capital expenditure changes from 246 billion to 250 billion

Answer 1

Δf ≈ df = f'(x₀)·Δx = 180(246)^-2/3·(250 - 246) = 1834 billion of dollars/billion of dolars of capital outlay