Examples for

Tangents & Normals

Secant lines, tangent lines and normal lines are straight lines that intersect a curve in different ways. A secant line is a line passing through two points of a curve. A line is considered a tangent line to a curve at a given point if it both intersects the curve at that point and its slope matches the instantaneous slope of the curve at that point. On a differentiable curve, as two points of a secant line approach each other, the secant line tends toward the tangent line. 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 secants, tangents and normals to a curve or a surface.

Secant Lines

Find a secant line to a curve.

Tangent Planes

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

Tangent Lines

Find a tangent line to a curve.

Tangent Hyperplanes

Find a hyperplane that is tangent to an abstract surface.

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Step-by-Step Solutions for Applications of Calculus

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• Derivatives
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• Normal Lines

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