\mbox{Wachstumsrate und Elastizität}

f

\ln f

\mbox{Tangente an } \ln f \mbox{ in } x_{0} \
T(x) = \ln f(x_{0}) + [\ln f]'(x_{0}) \cdot (x - x_{0})

$(x_{0}, f(x_{0}))$

= [ \ln f ]'(x_{0}) = \frac{f'(x_{0})}{f(x_{0})} = r(x_{0})

$= \ln f(x_{0}) - T(0) = [\ln f]' (x_{0}) \cdot x_{0} = x_{0} 
\cdot \frac{f'(x_{0})}{f(x_{0})} = \epsilon_{f, x_{0}}$

f(x) = x^(2)
g(x) = log(f(x))
A = Point(f)
B: (x(A), g(x(A)))
h = Tangent(B, g)
C = Intersect(h, yAxis)
D: (x(B), y(C))
Elastizität = Segment(B, D)
j = Segment(C, D)
E: (x(A) + 1, y(B))
F: (x(E), h(x(E)))
k = Segment(B, E)
Wachstumsrate = Segment(F, E)
G = Point(f)
H = Point(g)
I = Point(h)