$f(x) = e^x$

P

f(x) = e^x

$g(x) = e^{kx}$

strecken / stauchen

Neustart

$\overline{f}(x) = e^{-x}$

Q

k = 0.5 (slider from -5 to 5, step 0.1)
f(x) = ℯ^(x)
X0 = Point(xAxis)
x0: x(X0)
k0 = 1 (slider from 1 to 11, step 1)
kmin = If(k > 0, If[k > 1, 1, k], If[k > -1, -1, k])
kmax = If(k > 0, If[k > 1, k, 1], If[k > -1, k, -1])
diff: (kmax - kmin) / 10
k1 = If(k ≥ 1, kmin + ((k0 - 1) * diff), kmax - ((k0 - 1) * diff))
k2 = If(k > -1, kmin + ((k0 - 1) * diff), kmax - ((k0 - 1) * diff))
x1: x0 / k
X1: (x1, 0)
P0: (x0, f(x0))
Y0: (0, f(x0))
h(x) = ℯ^((k * x))
v = Vector(Y0, P0)
L = -3 (slider from -5 to 5, step 0.1)
g1(x) = ℯ^((k1 * x))
Text3: "k = " + k1 + ""
g2(x) = ℯ^((k2 * x))
f2(x) = ℯ^((-x))
Text2: "g(x) = e^{" + (LaTeX[k]) + "x}"
k3 = If(k > 0, k1, k2)
Text4: "k = " + k3 + ""
t_0(x) = (f'(x0) * (x - x0)) + f(x0)
Steigung = 1 (slider from -5 to 5, step 0.1)
T_0: (2, t_0(2))
Q0: (x(T_0) + 1, t_0(x(T_0) + 1))
R0: (x(Q0), y(T_0))
D0 = Polygon({T_0, R0, Q0})
t_1(x) = (h'(x1) * (x - x1)) + h(x1)
m0: f'(x0)
T_1 = Intersect(t_1, y = t_0(2))
Q1: (x(T_1) + 1 / k, t_1(x(T_1) + 1 / k))
R1: (x(Q1), y(T_1))
D1 = Polygon({T_1, R1, Q1})
m1: h'(x1)
Text7: "x_0 = " + x0 + ""
P1: (x1, h(x1))
Text8: "x_1 = \frac{x_0}{k} = " + (LaTeX[x1]) + ""
U2 = NaN
O2 = NaN
R = 1 (slider from -5 to 5, step 0.1)
Text6: "m = g'(0) = " + m1 + ""
Text5: "m = f'(0) = " + m0 + ""