Given \(\frac{dy}{dx} = x^3 - \frac{4}{x^2}\), we need to find \(\frac{dy}{dt}\) when \(x = 2\) and \(\frac{dx}{dt} = -0.05\).

First, calculate \(\frac{dy}{dx}\) at \(x = 2\):

\(\frac{dy}{dx} = 2^3 - \frac{4}{2^2} = 8 - 1 = 7\).

Using the chain rule, \(\frac{dy}{dt} = \frac{dy}{dx} \times \frac{dx}{dt}\).

Substitute the values: \(\frac{dy}{dt} = 7 \times (-0.05) = -0.35\).

Thus, the rate of change of the \(y\)-coordinate is \(-0.35\) units/s.