f(x) = - 1/2·(x - 3)^2 + 8 = - 0.5·x^2 + 3·x + 3.5
g(x) = 1/2·x + 7/2 = 0.5·x + 3.5
Differenzfunktion
d(x) = f(x) - g(x) = (- 0.5·x^2 + 3·x + 3.5) - (0.5·x + 3.5) = 2.5·x - 0.5·x^2
D(x) = 5·x^2/4 - x^3/6
Schnittstellen f(x) = g(x) bzw. d(x) = 0
2.5·x - 0.5·x^2 = 0
x = 5 ∨ x = 0
Fläche im Intervall von 0 bis 5
D(5) - D(0) = (5·5^2/4 - 5^3/6) - (5·0^2/4 - 0^3/6) = 125/12 = 10.42