## 2.6. Tangent to a Function of x

GeoGebra offers a command for the tangent to a function f(x) at x = a. Type the following lines into the input field and press the Enter key after each line.

a = 3

f(x) = 2 sin(x)

t = Tangent[a, f]

By animating number a (see Animation) the tangent slides along the graph of function f.

Here is another way of getting the tangent to a function f in a certain point T.

a = 3

f(x) = 2 sin(x)

T = (a, f(a))

t: X = T + s (1, f'(a))

This gives us point T on the graph of f whereby tangent t is given in parametric form.

By the way, you can create the tangent of a function geometrically too:

· Select mode New point and click on the graph of function f to get a new point A that lies on function f.

· Select mode Tangents and click successively on function f and on point A.

Now, select Move and drag point A along the function with your mouse. In this way you can observe the tangent changing dynamically too.

Related Topics

2. Examples

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