Skip to main content\(\newcommand{\deriv}[2]{\displaystyle \frac{d#1}{d#2}}
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Instructions.
Drag the red point anywhere in the plane. The gradient vector
\(\nabla f = 2x\,\mathbf i + 2y\,\mathbf j\) of
\(f(x,y) = 1 + x^2 + y^2\) is drawn at the point, together with the level curve of
\(f\) through the point. Observe that the gradient is always perpendicular to the level curve and points in the direction in which
\(f\) increases.