Realtiv sicher lassen sich die Informationen
f ( x ) = a*x^3 + b * x^2 + c * x + d
f ( 0 ) = -1 => d = -1
f ( x ) = a*x^3 + b * x^2 + c * x -1
f ( 4 ) = 3
f ´( x ) = 3 * a * x^2 + 2 * b * x + c
f ´( 0 ) = 0 => c = 0
f ( x ) = a*x^3 + b * x^2 -1
f ´( x ) = 3 * a * x^2 + 2 * b * x
f ( 4 ) = 3
f ´( 4 ) = 0
a*64 + b*16 -1 = 3
3 * a * 16 + 2 * b * 4 = 0
b = 3/4
a = -1/8
~plot~ -1/8 * x^3 + 3/4 * x^2 -1 ~plot~