bonjour,
g(x)=-0.1x²+1.4x+1.5
-0.1(x+1)(x-15)=-0.1(x²+x-15x-15)
-0.1(x²-14x-15)=-0.1x²+1.4x+1.5
g(x)=-0.1(x+1)(x-15)
-0.1(x-7)²+32/5=-0.1(x²-14x+49)+6.4
-0.1x²+1.4x-4.9+6.4
-0.1x²+1.4x+1.5
g(x)=-0.1(x-7)²+32/5
g(0)=-0.1(0²)+1.4(0)+1.5
g(0)=1.5
g(7)=-0.1(x-7)²+32/5
g(7)=-0.1(0)²+32/5
g(7)=32/5
g(7)=6.4
g(x)=1.5
-0.1x²+1.4x+1.5=1.5
-0.1x+1.4x=1.5-1.5
-0.1x²+1.4x=0
x(-0.1x+1.4)=0 x=0
-0.1x+1.4=0 -0.1x=-1.4 x=1.4/0.1 x=14
g(x)=-0.1(x+1)(x-15)
x -∞ -1 +15 +∞
x+1 - 0 + + +
x-15 - - 0 +
-0.1(x+1)(x-15) - 0 + 0 -
g(x)≥0 x ∈[-1,+15]
g(x)=-0.1x²+1.4x+1.5
a<0 alors g(x) admet un maximum
a(x-α)²+β
(α;β) coordonnées du maximum
α=-b/2a
α=1.4/-0.2
α=7
β=g(α)
β=g(7)
g(7)=6.4
voir plus haut
β=6.4
maximum(7;6.4)
hauteur maximale 6.4
