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# Applying A Math Differentiation Maxima and Minima in Minecraft

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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?

## Solution

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 $A = (25)(25) = 625 m^2$.