Prove that the inequality

x (x + 1) (x + 2) (x + 3) ≥ - 1

holds for all real numbers x.

(x²+x) (x²+5x+6) = x^4 + 6x³ + 11x² + 6x + 1 ≥0

f (x) = x^4 + 6x³ + 11x² + 6x + 1

f' (x) = 4x³ + 18x² + 22x + 6

racines x1 = - 0,301 x2 = - 1,5 x3 = - 2,618

variations

x - 2,62 - 1,5 - 0,3

f' (x) - 0 + 0 - 0 +

f (x) - inf / 0 / / 0 /

on voit que cette fonction st toujours positive