Bonjour,

1)

Si, f(x)=1/2(x-8)²+2 ∀x∈[5;11]

f(x)-5/2=1/2(x-8)²+2-5/2

           =1/2(x-8)²+1/2*(4)-1/2*(5)

           =1/2((x-8)²+4-5)

           =1/2(x²-16x+64+4-5)

           =1/2(x²-16x+63)

f(x)-5/2=1/2(x-7)(x-9)

2)

f(x)<5/2  <=> f(x)-5/2<0

              <=> 1/2(x-7)(x-9)<0

              <=> (x-7)(x-9)<0

f(x)<5/2  <=>  7<x<9