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tangent (graph)

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Tangent (graph)


In graphs, a straight line that touches a curve and gives the gradient of the curve at the point of contact. At a maximum, minimum, or point of inflection, the tangent to a curve has zero gradient.

To find the gradient of the tangent of the curve at point P, extend the tangent AC and construct the right-angled triangle ABC:

The gradient of the tangent at the point P is AB/BC. This is only an approximation. To make the answer as accurate as possible, the length of the tangent AC should be large.

For example, to find the gradient of the curve y = x2 - 2x at the point P(2,0):

P = AB/BC = 5/2.5 = 2

See also tangent (trigonometry) and tangent (circle).

© Research Machines plc 2008. All rights reserved. Helicon Publishing is a division of Research Machines plc.


 
 

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