Square

# Applying A Math Differentiation Maxima and Minima in Minecraft

Looking for JC H2 tuition?

Β  Β orΒ  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?

## Solution

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

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

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

Substitute eqn β  into β‘, 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 β .
The maximum area $A = (25)(25) = 625 m^2$.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://ingelsoong.com/a-math-differentiation-maxima-minima-minecraft/", "fetch_time": 1718469120000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-26/segments/1718198861605.77/warc/CC-MAIN-20240615155712-20240615185712-00640.warc.gz", "warc_record_offset": 289533604, "warc_record_length": 30083, "token_count": 275, "char_count": 832, "score": 4.25, "int_score": 4, "crawl": "CC-MAIN-2024-26", "snapshot_type": "latest", "language": "en", "language_score": 0.8412052989006042, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00009-of-00064.parquet"}