The 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].

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.

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).

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.

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.

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