f(x) =

f(x)=

x

x_0

$f(x)$

$f(x_0)$

Sekante anzeigen

Tangente anzeigen

$x$

$x_0$

f(x) = (0.05 * (x^(3) + (0.5 * ℯ^(x)))) + 0.4 + (0.1 * x)
funktionstextbox = Textfield(f)
q = 2.81 (slider from -5 to 5, step 0.01)
p = 2 (slider from -5 to 5, step 0.01)
Q: (q, f(q))
P: (p, f(p))
Q_{0}: (0, f(q))
P_{0}: (0, f(p))
g = Segment(Q_{0}, Q)
h = Segment(P, P_{0})
i = Line(P, Q)
PQ: (x(Q), y(P))
j = Segment(P, PQ)
k = Segment(Q, PQ)
dy: f(q) - f(p)
dx: q - p
m: dy / dx
f_{q}: f(q)
f_{p}: f(p)
l = Tangent(P, f)
a = true
b = true
X_{q}: (q, 0)
X_{p}: (p, 0)
n = Segment(X_{p}, P)
r = Segment(X_{q}, PQ)
textp: "" + (If[p < 0, "+", "-"] + (abs(p))) + ""
textfp: If[f(p) < 0, "+", "-"] + (abs(f(p)))
steigungstext = If(dx ≟ 0, "\;nicht\;definiert", "=" + m)
Text1: "m=\frac{f(x)-f(x_0)}{x-x_0}=\frac{" + (LaTeX[f_{q}]) + "" + (LaTeX[textfp]) + "}{" + (LaTeX[q]) + "" + (LaTeX[textp]) + "}=\frac{" + (LaTeX[dy]) + "}{" + (LaTeX[dx]) + "}" + (LaTeX[steigungstext]) + ""