Examples for

Tangents & Normals

Tangent lines are straight lines that pass through a given curve and have the slope of the curve at the point where they intersect. The idea of tangent lines can be extended to higher dimensions in the form of tangent planes and tangent hyperplanes. A normal line is a line that is perpendicular to the tangent line or tangent plane. Wolfram|Alpha can help easily find the equations of tangents and normals to a curve or a surface.

Tangent Lines

Find a tangent line to a curve.

Find the tangent to the graph of a function at a point:

Find the tangent to a curve specified by an equation:

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Tangent Planes

Find a plane that is tangent to a surface in 3D.

Find the tangent plane to a surface:

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Tangent Hyperplanes

Find a hyperplane that is tangent to an abstract surface.

Find a tangent hyperplane:

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Normal Lines

Find a line that is perpendicular to the tangent line to an equation at a point.

Find the normal line to the graph of a function at a point:

Find the normal to a curve specified by an equation:

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