Skip to main content\(\newcommand{\deriv}[2]{\displaystyle \frac{d#1}{d#2}}
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Instructions.
Drag the unit vector
\(\mathbf u\) around the point
\(P_0(1,1)\) on the level-curve plot of
\(f(x,y) = \frac{x^2}{2} + \frac{y^2}{2}\) and watch the value of
\(D_{\mathbf u} f = u_1 + u_2\text{.}\) Use the buttons to snap
\(\mathbf u\) to the answers of Example III: the direction of fastest increase, the direction of fastest decrease, and the two directions of no change.