B'

B

B(x)

B'(x)

Änderungsrate B'(x)

Bestand B(x)

+

+

+

a

b

f1(x) = If[0 ≤ x ≤ 2, 2, 0]
Intervall = Segment((0 | 0), (8 | 0))
f2(x) = If[2 < x ≤ 3, 0, 0]
f3(x) = If[3 < x ≤ 5, -1.5, 0]
f4(x) = If[5 < x ≤ 8, 1, 0]
f0(x) = f1(x) + f2(x) + f3(x) + f4(x)
f(x) = If[0 ≤ x ≤ 8, f0(x)]
a: 1
Intervallpunkte = Sequence((a + (i * 1) | 0), i, 0, 8)
X = Point(Intervallpunkte)
t: x(X)
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 ≤ 8, x - 5 + I3(5), 0]
I0(x) = I1(x) + I2(x) + I3(x) + I4(x)
I(x) = If[0 ≤ x ≤ 7, I0(x)]
fa(x) = f(x - a)
OF = Integral(fa, a, t)
Y: (x(X) | OF)
gl1: x = x(X)
Z: (x(X) | f(x(X)))
ul2 = If(2 + a < t ≤ 3 + a, ((t - (2 + a)) * fa(t)), 0)
ul1 = If(0 + a ≤ t ≤ 2 + a, ((t - a) * fa(t)), 4)
ul3 = If(3 + a < t ≤ 5 + a, ((t - (3 + a)) * fa(t)), -3)
ul4: ((t - (a + 5)) * fa(t))
t1 = If(a + 0 ≤ t ≤ a + 2, t, a + 2)
t2 = If(a + 2 < t ≤ a + 3, t, a + 3)
t3 = If(a + 3 < t ≤ a + 5, t, a + 5)
t4 = If(a + 5 < t ≤ a + 8, t, a + 8)
t3o = If(3 < t ≤ 5, t, 5)
I1z(x) = If[a ≤ x ≤ a + 2, I1(x - a)]
I2z(x) = If[a + 2 < x ≤ a + 3, I2(x - a)]
I3z(x) = If[a + 3 < x ≤ a + 5, I3(x - a)]
Text3: "\underbrace{2 \cdot (" + (LaTeX[t1]) + "-" + (LaTeX[a]) + ")}_{" + (LaTeX[ul1]) + "}"
X0: (a | 0)
A1 = Integral(fa, a, t1)
A2 = Integral(fa, a + 2, t2)
A3 = Integral(fa, a + 3, t3)
A4 = Integral(fa, a + 5, t4)
Text5: "\underbrace{0 \cdot (" + (LaTeX[t2]) + "-" + (LaTeX[a + 2]) + ")}_{" + (LaTeX[ul2]) + "}"
Text6: "\underbrace{(-1.5) \cdot (" + (LaTeX[t3]) + "-" + (LaTeX[a + 3]) + ")}_{" + (LaTeX[ul3]) + "} "
Text7: "\underbrace{1 \cdot (" + (LaTeX[t4]) + "-" + (LaTeX[a + 5]) + ")}_{" + (LaTeX[ul4]) + "} "
I4z(x) = If[a + 5 < x ≤ a + 8, I4(x - a)]
gL: -1
gR: 14
Text4: "\underbrace{B_{" + (LaTeX[a]) + "}^{" + (LaTeX[t]) + "}}_{" + (LaTeX[y(Y)]) + "} = "
gUu: -2.5
gOu: 3.5
gUo: -2
gOo: 5
X1: (9 | 0)