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# 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.