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.

Note by Yumi Zhang
2 years, 1 month ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest


Xu Kesi - 2 years, 1 month ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...