B'

x

B

B(x)

B'(x)

Änderungsrate B'(x)

Bestand B(x)

+

+

+

f1(x) = If[0 ≤ x ≤ 2, 2, 0]
Intervallpunkte = Sequence(((i * 0.5) | 0), i, 0, 14)
Intervall = Segment((0 | 0), (7 | 0))
f2(x) = If[2 < x ≤ 3, 0, 0]
f3(x) = If[3 < x ≤ 5, -1.5, 0]
f4(x) = If[5 < x ≤ 7, 1, 0]
f0(x) = f1(x) + f2(x) + f3(x) + f4(x)
f(x) = If[0 ≤ x ≤ 7, f0(x)]
X = Point(Intervallpunkte)
t: x(X)
OF = Integral(f, 0, t)
I1(x) = If[0 ≤ x ≤ 2, (2 * x), 0]
I2(x) = If[2 < x ≤ 3, (0 * (x - 2)) + I1(2), 0]
I3(x) = If[3 < x ≤ 5, (-1.5 * (x - 3)) + I2(3), 0]
I4(x) = If[5 < x ≤ 7, x - 5 + I3(5), 0]
I0(x) = I1(x) + I2(x) + I3(x) + I4(x)
I(x) = If[0 ≤ x ≤ 7, I0(x)]
Y: (x(X) | OF)
gl1: x = x(X)
Z: (x(X) | f(x(X)))
ul2 = If(2 < t ≤ 3, ((t - 2) * f(t)), 0)
ul1 = If(0 ≤ t ≤ 2, ((t - 0) * f(t)), 4)
ul3 = If(3 < t ≤ 5, ((t - 3) * f(t)), -3)
ul4: ((t - 5) * f(t))
t1 = If(0 ≤ t ≤ 2, t, 2)
Text3: "\underbrace{2 \cdot (" + (LaTeX[t1]) + "-0)}_{" + (LaTeX[ul1]) + "}"
t2 = If(2 < t ≤ 3, t, 3)
t3 = If(3 < t ≤ 5, t, 5)
t4 = If(5 < t ≤ 7, t, 7)
Text5: "\underbrace{0 \cdot (" + (LaTeX[t2]) + "-2)}_{" + (LaTeX[ul2]) + "}"
Text6: "\underbrace{(-1.5) \cdot (" + (LaTeX[t3]) + "-3)}_{" + (LaTeX[ul3]) + "} "
Text7: "\underbrace{1 \cdot (" + (LaTeX[t4]) + "-5)}_{" + (LaTeX[ul4]) + "} "
A1 = Integral(f, 0, t1)
A2 = Integral(f, 2, t2)
t3o = If(3 < t ≤ 5, t, 5)
A3 = Integral(f, 3, t3o)
A4 = Integral(f, 5, t4)
I1z(x) = If[0 ≤ x ≤ 2, I1(x)]
I2z(x) = If[2 < x ≤ 3, I2(x)]
I3z(x) = If[3 < x ≤ 5, I3(x)]
I4z(x) = If[5 < x ≤ 7, I4(x)]
Text4: "\underbrace{B(" + (LaTeX[t]) + ")}_{" + (LaTeX[y(Y)]) + "} = "