Geogebra 里怎样作过函数图象外一点切线？

isee

源自知乎提问

以前碰到过，但无伤大雅，往往是置之不理.



法1 通常用命令 Tangent((1,-2),y=x^2) 之类即可：过点 (1,-2) 作 曲线 y=x^2 的切线.

法2 如果习惯用鼠标操作，则输入曲线 y-x^2=0，点 (1,-2)，然后用工具栏的 Tangents.

法3 (先算出切线方程，然后) 输入即可



Geogebra 手册自带 Tangent 帮忙 Tangent Command - GeoGebra Manual

Tangent( <Point>, <Conic> )Creates (all) tangents through the point to the conic section.
Example: Tangent((5, 4), 4x^2 - 5y^2 = 20) yields x - y = 1.
Tangent( <Point>, <Function> )Creates the tangent to the function atx = x(A).
Note: x(A) is the x-coordinate of the given point A.
Example: Tangent((1, 0), x^2) yields y = 2x - 1.
Tangent( <Point on Curve>, <Curve> )Creates the tangent to the curve in the given point.
Example: Tangent((0, 1), Curve(cos(t), sin(t), t, 0, π)) yields y = 1.
Tangent( <x-Value>, <Function> )Creates the tangent to the function atx-Value.
Example: Tangent(1, x^2) yields y = 2x - 1.
Tangent( <Line>, <Conic> )Creates (all) tangents to the conic section that are parallel to the given line.
Example: Tangent(y = 4, x^2 + y^2 = 4) yields y = 2 and y = -2.
Tangent( <Circle>, <Circle> )Creates the common tangents to the two Circles (up to 4).
Example: Tangent(x^2 + y^2 = 4, (x - 6)^2 + y^2 = 4) yields y = 2, y = -2, 1.49x + 1.67y = 4.47 and -1.49x + 1.67y = -4.47.
Tangent( <Point>, <Spline> )Creates the tangent to the spline in the given point.
Example: Let A = (0, 1), B = (4, 4) and C = (0, 4). Tangent(A, Spline({A, B, C})) yields line a: y = 0.59x + 1.
Tangent( <Point>, <Implicit Curve> )Creates the tangent to the implicit curve in the given point.
Example: Tangent((1,1), x^2+y^2=1)) yields lines x=1 and y=1.