Question

Berechnen Sie die mittlere Steigung der Funktion f in jedem der drei Intervalle

(Nur Bild 1 ) 

Answer 1

f(x) = 1/x
m1 = (f(1) - f(0.5)) / (1 - 0.5) = -2
m2 = (f(2) - f(1)) / (2 - 1) = -0.5
m3 = (f(3) - f(2)) / (3 - 2) = -1/6 = -0.1667

f(x) = √x
m1 = (f(1) - f(0)) / (1 - 0) = 1
m2 = (f(2) - f(1)) / (2 - 1) = √2 - 1 = 0.4142
m3 = (f(4) - f(2)) / (4 - 2) = 1 - √2/2 = 0.2929

f(x) = SIN(x)
m1 = (f(1) - f(0)) / (1 - 0) = SIN(1) = 0.8415
m2 = (f(pi - 1) - f(1)) / ((pi - 1) - 1) = 0
m3 = (f(pi) - f(pi - 1)) / (pi - (pi - 1)) = -SIN(1) = -0.8415