Use GSP to solve problems about FUNCTION

In order to treat with this disgusting problem on the homepage,I have tried some different methods, including a few experiment. Finally I found a really EASY way. I first expressed the function of the height of the gravity with the parameter 'h'. f(h)=[36h(h/2)+120]/(36h+12)=3h^2+20/(6h+2) (h≥0) Then I expressed the derived function of f(h) (h≥0) and found out the points when the derived function is ZERO, while f(h) is at the smallest value. GSP is a very interesting and professional softwere which can build geometrical graphs, even the image of a function. So I can find the position of the "SMALLEST-VALUE-POINT" quickly by searching on the visible interface.I got the answer of 2.27.Though it cannot be completely precision, It's enough for this exercise and most other applications.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

同志好.

Xu Kesi - 2 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$