f = (x3-8) / (2*x2-8)
umformen
f = (x3-8) * (2*x2-8)(^-1)
u = x3 - 8
u ´ = 3*x2
v = (2*x2-8)(^-1)
v´ = (-1)(2*x2-8)(^-2) * 4x
v´ = (-4x*)(2*x2-8)(^-2)
( u * v ) ´ u´ * v + u * v´
3*x2 * (2*x2-8)(^-1) + ( x3 - 8 ) * (-4x*) * (2*x2-8)^(-2)
3*x2 / (2*x2-8 )^(-1) + ( -4*x4 + 32*x ) / (2*x2-8)^(-2)
3*x2 * (2*x2-8 ) / (2*x2-8 )^(-2) + ( -4*x4 + 32*x ) / (2*x2-8)^(-2)
( 6*x4 - 24x2 -4*x4 + 32*x ) / (2*x2-8)^(-2)
( 2*x4 - 24x2 + 32*x ) / (2*x2-8)^(-2)
Extremwert : Zähler = 0
2*x4 - 24x2 + 32*x = 0
Satz vom Nullprodukt anwenden
x * ( 2*x3 - 24x + 32 ) = 0
x = 0
und
2*x3 - 24x + 32 = 0
x3 - 12x + 16 = 0
Raten oder Probieren
x = -4
(-4)3 - 12 *(-4) + 16 = 0
-64 + 48 + 16 = 0 stimmt
x = 0
und
x = -4