What is the maximum height of the plant?

$y=4x-\frac{x^2}{2}$

so $\frac{dy}{dx}=4-x$ so $4-x=0⇒x=4$

$\frac{d^2y}{dx^2}=-1<0$ so, at $x=4$ days plant achieves max. height

given by $y(4) = 4×4-\frac{4^2}{2}=8cm$