WeBWorK Standalone Renderer

The surface $z = g(x,y)$ and the red point $(2,1,2)$ are shown in the figure. Determine if the following directional derivatives $g_{\vec{u}} \, (2,1)$ are positive, negative, zero, or do not make sense (because something is wrong with $\vec{u}$ ).

Note: The directional derivative is also often written as $D_{\vec{u}} \, g(a,b)$ .

1. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = (\vec{j} - \vec{i})/ \sqrt{2}$ .

2. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = -\vec{i}$ .

3. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = 2\vec{i}+\vec{j}$ .

4. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = (\vec{i}-2\vec{j})/\sqrt{5}$ .

5. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = (\vec{i} + \vec{j})/ \sqrt{2}$ .

6. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = (\vec{i} - \vec{j})/ \sqrt{2}$ .

7. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = (\vec{i}-\vec{k}) / \sqrt{2}$ .

8. $g_{\vec{u}} \,(2,1)$ where $\vec{u} = -\vec{j}$ .

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You can earn 50% partial credit for 4 - 5 correct answers, and 75% partial credit for 6 - 7 correct answers.