# Subtangent

The subtangent is a term from analytical geometry . We consider a point on a differentiable curve (red) and form the tangent (green). The projection of the tangent onto the abscissa is then called the subtangent (yellow in the picture).

If a curve is differentiable at one point , the subtangent is the distance between the point on the abscissa and the zero point of the tangent. ${\ displaystyle x_ {0}}$ ${\ displaystyle x_ {0}}$ The zero and thus the subtangent can be obtained via the equation of the tangent${\ displaystyle t (x) = f '(x_ {0}) \ cdot (x-x_ {0}) + f (x_ {0})}$ ${\ displaystyle x_ {s} = {\ frac {-f (x_ {0})} {f '(x_ {0})}} + x_ {0}}$ ${\ displaystyle \ left | {\ frac {f (x_ {0})} {f '(x_ {0})}} \ right |.}$ The amount of the subtangent of the function is constant 1 for all tangents, since: ${\ displaystyle e}$ ${\ displaystyle f (x) = e ^ {x}}$ ${\ displaystyle \ left | {\ frac {e ^ {x_ {0}}} {e ^ {x_ {0}}}} \ right | = 1}$ As an analogy to the normal there are the subnormal .