search
HomeSoftware TutorialComputer SoftwareThe method of finding the extreme value of a function based on drawing the derivative function image in the geometric sketchpad

When drawing, it is particularly important to find the extreme value of the function. Geometry Sketchpad provides us with a method to find the extreme value of a function based on the image of the derivative function. This method works not only for simple functions, but also for complex functions. In order to help everyone understand this method in depth, PHP editor Xinyi will explain its principles and steps in detail below.

1. Open the geometric sketchpad, [Draw] - [Draw New Function], enter the function analytical formula in the figure below in the function editor, and click [OK].

The method of finding the extreme value of a function based on drawing the derivative function image in the geometric sketchpad

2. Right-click the analytical formula of the function, select [Define Derivative Function], and the analytical formula of the derivative function will appear. Right-click the derivative function and select [Draw Function]. The derivative function (blue) of the original function will appear in the drawing area.

The method of finding the extreme value of a function based on drawing the derivative function image in the geometric sketchpad

3. Select the drawn derivative function image and the x-axis, [Construct] - [Intersection] to get point A. Because the original function is not differentiable at point B, [Draw] - [Draw Point], draw point B (-4, 0).

The method of finding the extreme value of a function based on drawing the derivative function image in the geometric sketchpad

4. Select point B and point A, [Metric] - [Abscissa], the abscissa value is the abscissa of the turning point of the monotonic interval of the original function.

The method of finding the extreme value of a function based on drawing the derivative function image in the geometric sketchpad

Explanation: At the drawing point B, the derivative does not exist, so the original function has a maximum value of 0 at point B and a minimum value at point A.

The above is the detailed content of The method of finding the extreme value of a function based on drawing the derivative function image in the geometric sketchpad. For more information, please follow other related articles on the PHP Chinese website!

Statement
This article is reproduced at:zol. If there is any infringement, please contact admin@php.cn delete
How much does Microsoft PowerToys cost?How much does Microsoft PowerToys cost?Apr 09, 2025 am 12:03 AM

Microsoft PowerToys is free. This collection of tools developed by Microsoft is designed to enhance Windows system functions and improve user productivity. By installing and using features such as FancyZones, users can customize window layouts and optimize workflows.

What is the best alternative to PowerToys?What is the best alternative to PowerToys?Apr 08, 2025 am 12:17 AM

ThebestalternativestoPowerToysforWindowsusersareAutoHotkey,WindowGrid,andWinaeroTweaker.1)AutoHotkeyoffersextensivescriptingforautomation.2)WindowGridprovidesintuitivegrid-basedwindowmanagement.3)WinaeroTweakerallowsdeepcustomizationofWindowssettings

Does Microsoft PowerToys require a license?Does Microsoft PowerToys require a license?Apr 07, 2025 am 12:04 AM

Microsoft PowerToys does not require a license and is a free open source software. 1.PowerToys provides a variety of tools, such as FancyZones for window management, PowerRename for batch renaming, and ColorPicker for color selection. 2. Users can enable or disable these tools according to their needs to improve work efficiency.

Is Microsoft PowerToys free or paid?Is Microsoft PowerToys free or paid?Apr 06, 2025 am 12:14 AM

Microsoft PowerToys is completely free. This tool set provides open source utilities that enhance Windows operating system, including features such as FancyZones, PowerRename, and KeyboardManager, to help users improve productivity and customize their operating experience.

Is PowerToys part of Windows 11?Is PowerToys part of Windows 11?Apr 05, 2025 am 12:03 AM

PowerToys is not the default component of Windows 11, but a set of tools developed by Microsoft that needs to be downloaded separately. 1) It provides features such as FancyZones and Awake to improve user productivity. 2) Pay attention to possible software conflicts and performance impacts when using them. 3) It is recommended to selectively enable the tool and periodically update it to optimize performance.

How do I download Microsoft PowerToys?How do I download Microsoft PowerToys?Apr 04, 2025 am 12:03 AM

The way to download Microsoft PowerToys is: 1. Open PowerShell and run wingetinstallMicrosoft.PowerToys, 2. or visit the GitHub page to download the installation package. PowerToys is a set of tools to improve Windows user productivity. It includes features such as FancyZones and PowerRename, which can be installed through winget or graphical interface.

What is the purpose of PowerToys?What is the purpose of PowerToys?Apr 03, 2025 am 12:10 AM

PowerToys is a free collection of tools launched by Microsoft to enhance productivity and system control for Windows users. It provides features through standalone modules such as FancyZones management window layout and PowerRename batch renaming files, making user workflow smoother.

Does PowerToys need to be running?Does PowerToys need to be running?Apr 02, 2025 pm 04:41 PM

PowerToys needs to be run in the background to achieve its full functionality. 1) It relies on system-level hooks and event listening, such as FancyZones monitoring window movement. 2) Reasonable resource usage, usually 50-100MB of memory, and almost zero CPU usage when idle. 3) You can set up power-on and use PowerShell scripts to implement it. 4) When encountering problems, check the log files, disable specific tools, and ensure that they are updated to the latest version. 5) Optimization suggestions include disabling infrequently used tools, adjusting settings, and monitoring resource usage.

See all articles

Hot AI Tools

Undresser.AI Undress

Undresser.AI Undress

AI-powered app for creating realistic nude photos

AI Clothes Remover

AI Clothes Remover

Online AI tool for removing clothes from photos.

Undress AI Tool

Undress AI Tool

Undress images for free

Clothoff.io

Clothoff.io

AI clothes remover

Video Face Swap

Video Face Swap

Swap faces in any video effortlessly with our completely free AI face swap tool!

Hot Tools

Dreamweaver CS6

Dreamweaver CS6

Visual web development tools

SublimeText3 English version

SublimeText3 English version

Recommended: Win version, supports code prompts!

mPDF

mPDF

mPDF is a PHP library that can generate PDF files from UTF-8 encoded HTML. The original author, Ian Back, wrote mPDF to output PDF files "on the fly" from his website and handle different languages. It is slower than original scripts like HTML2FPDF and produces larger files when using Unicode fonts, but supports CSS styles etc. and has a lot of enhancements. Supports almost all languages, including RTL (Arabic and Hebrew) and CJK (Chinese, Japanese and Korean). Supports nested block-level elements (such as P, DIV),

EditPlus Chinese cracked version

EditPlus Chinese cracked version

Small size, syntax highlighting, does not support code prompt function

SAP NetWeaver Server Adapter for Eclipse

SAP NetWeaver Server Adapter for Eclipse

Integrate Eclipse with SAP NetWeaver application server.