Hallo
K(x) = k3 x^3 +k2 x^2 +k1 x +k0 = x³ -5 x² +11 x +5
k3 = 1
k2 = -5
k1 = 11
k0 = 5
E(x) = e1 x = 10 x
e1 = 10
G(x) = -k3 x^3 -k2 x^2 +(e1 -k1) x -k0 = -x^3 +5 x^2 - x -5
G'(x) = -3 k3 x^2 -2 k2 x +(e1 -k1)
G'(xGminmax) = 0 => 3 k3 x^2 +2 k2 x +(k1 -e1) = 0
xGminmax = +1/(3 k3) *( -k2 +/- (k2^2 -3k3 (k1 -e1))^0.5 )
xGminmax = +1/(3*1) * (+5 +/- (25 -3*1* (11 -10))^0.5)
xGminmax = 1/3 *( 5 +/- (25 -3)^0.5) = 1/3 *( 5 +/- (22)^0.5)
= 1/3 * (5 +/- 4.69041576) = 0.103194746 oder 3.230138587
G(xGminmax1) = -xGminmax1^3 +5 xGminmax1^2 - xGminmax1 -5 = -5.051047905
G(xGminmax2) = -xGminmax2^3 +5 xGminmax2^2 - xGminmax2 -5 = 10.23623309