Bonjour
Supersong
b) Cm(q) = C(q) - C(q-1)
Or
[tex]\boxed{C(q)=q^3-88,5q^2+2710,5q+3000}[/tex]
et
[tex]C(q-1)=(q-1)^3-88,5(q-1)^2+2710,5(q-1)+3000\\\\=(q^3-3q^2+3q-1)-88,5(q^2-2q+1)+2710,5(q-1)+3000\\\\=q^3-3q^2+3q-1-88,5q^2+177q-88,5+2710,5q-2710,5+3000\\\\=q^3-88,5q^2+2710,5q+3000-3q^2+3q-1+177q-88,5-2710,5\\\\\boxed{C(q-1)=q^3-88,5q^2+2710,5q+3000-3q^2+180q-2800}[/tex]
D'où,
[tex]C_m(q)=C(q)-C(q-1)\\\\=(q^3-88,5q^2+2710,5q+3000)\\\\\ -(q^3-88,5q^2+2710,5q+3000-3q^2+180q-2800)\\\\\\C_m(q)=q^3-88,5q^2+2710,5q+3000\\\\\ -q^3+88,5q^2-2710,5q-3000+3q^2-180q+2800\\\\\\\boxed{C_m(q)=3q^2-180q+2800}[/tex]
De plus,
[tex]C_m(q)=3q^2-180q+2800\\\\C_m(q)=3(q^2-60q)+2800\\\\C_m(q)=3(q^2-60q+900-900)+2800\\\\C_m(q)=3(q^2-60q+900)-3\times900+2800\\\\C_m(q)=3(q^2-2\times30\times q+30^2)-2700+2800\\\\\boxed{C_m(q)=3(q-30)^2+100}[/tex]
