Tangent to a function of x

GeoGebra offers a command for the tangent to a function f(x) at x=a.

    a = 3
    f(x) = 2 sin(x)
    t = Tangent[a, f]

By animating a (see 4.1.2) the tangent slides along the graph of f.

Another way of doing this would be

    a = 3
    f(x) = 2 sin(x)
    T = (a, f(a))
    t : X = T + s (1, f'(a))

Additionally, we get the point T on the graph of f. The tangent t is given in parametric form. By the way, you can create the tangent of a function geometrically too:

• Choose the mode New point (see 3.2) and click on the graph of the function f.

• Choose the mode Tangents and click on the function f and then on the point created before.

Now, choose the Move mode and drag the point along the function with your mouse. The tangent is changed dynamically too.