This applet shows the [b]directional derivative[/b] of f in the direction of [math]\vec{r}[/math].[br][br][b]Task[br][/b]Move [b][color=#0000ff]point P'[/color][/b] and[b] [color=#0000ff]Q'[/color][/b] and watch how the directional derivative changes for different points and for different directions.[br][br]Show the tangent plane and the inteersecting plane.[br]Show the directional derivative for [math]\vec{r} = \binom{1}{0}[/math] and [math]\vec{r} = \binom{0}{1}[/math].[br][br][b]Additional question[br][/b]How does the directional derivative change when the direction vector [math]\vec{r}[/math] is change to [math]2·\vec{r}[/math] or [math]3·\vec{r}[/math]?