(i) Plant Growth Rate:
The rate of plant growth concerning sunlight is determined by the derivative of the height function \(y\) with respect to time \(x\).
The height function is defined as:
\[
y = 4x - \frac{1}{2} x^2.
\]
Differentiating \(y\) with respect to \(x\) yields:
\[
\frac{dy}{dx} = 4 - x.
\]
Therefore, the rate of plant growth with respect to sunlight is:
\[
\frac{dy}{dx} = 4 - x.
\]
(ii) Maximum Plant Height:
To ascertain the time at which the plant attains its maximum height, we equate the rate of growth \(\frac{dy}{dx}\) to zero:
\[
4 - x = 0 \quad \Rightarrow \quad x = 4.
\]
Consequently, the plant reaches its maximum height after 4 days.
Substituting \(x = 4\) into the height equation provides the maximum height:
\[
y = 4(4) - \frac{1}{2} (4)^2 = 16 - 8 = 8 \, \text{cm}.
\]
The maximum height achieved by the plant is 8 cm.