Applying A Math Differentiation Maxima and Minima in Minecraft

Follow Ingel on instagram and telegram for FREE study notes and exam hacks!

Looking for JC H2 tuition?

Call or WhatsApp Ingel at 96726733 now to avoid disappointment!

See how A Math Differentiation Maxima and Minima can be applied in games:

Question

If you decide to craft 100m of fence to keep your animals in Minecraft, what is the largest rectilinear area you can fence up?

Let x be the length of the rectangle while y be the breadth.

The perimeter P is given by 2x + 2y = 100
or $x = 50 – y — ①$

The area A, which you need to maximise is $A = xy — ②$

Substitute eqn ① into ②, we have
$A = (50-y)y$

Differentiating with respect to y,
$ \frac{dA}{dy} = 50 – 2y $

Setting to $ \frac{dA}{dy} = 0 $,
$50 – 2y = 0,$
$y = 25$ and therefore $x = 50 – 25 = 25$ from eqn ①.
The maximum area $ A = (25)(25) = 625 m^2$.