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Tangents and normals
Tangents and Normals A tangent of a point $P(x, y)$ is the line that best approaches the point as $x$ approaches $x_0$. The normal to a point is the...
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Tangents and Normals A tangent of a point $P(x, y)$ is the line that best approaches the point as $x$ approaches $x_0$. The normal to a point is the...
Tangents and Normals
A tangent of a point is the line that best approaches the point as approaches . The normal to a point is the line that is perpendicular to the tangent and passes through the point.
The slope of the tangent is the derivative of the function that describes the curve at the point. The derivative of a function is a measure of how quickly its output changes with respect to its input.
The normal to a point is found by taking the negative reciprocal of the slope of the tangent.
Examples:
The tangent line to the curve at the point is .
The normal to the curve at the point is .
The tangent and normal to the curve at the point are found by finding the derivative and then finding the negative reciprocal of that