Skip to main content\(\newcommand{\R}{\mathbb{R}}
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A three dimensional plot of a curved surface shown in gray above a set of axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\text{.}\) The gray surface decreases as you move away from from a maximum near the z-axis. An arrow is shown below the surface on the xy-plane in red and points in the direction of the x and y axes. A gray segment is drawn from the beginning point of the red arrow, parallel to the z-axis, up to the surface. A point where the gray segment intersects the surface his highlighted. A blue plane is shown extending from the red arrow parallel to the z-axis, through the surface. The curve along the surface that is above the red segment and is the intersection between the curved surface and the blue plane is drawn in blue. This blue curve initially increases in z then decreases. The line segment that begins at the highlighted point and is tangent to the blue curve is shown in black.