# 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 .