Dérivation, accroissement et calcul marginal

•
t f(t)
•
f(t) = t2
•
52−42= 9
(4,5)2−42= 4,25
52−(4,5)2= 4,75
•

∆t
f(t+ ∆t)−f(t)
∆t
f(4 + ∆t)−f(4)
∆t=(4 + ∆t)2−(4)2 ∆t= 8 + ∆t
∆t→0
8+∆t−→
∆t→08

f(x)I
•f(x)
f x
•f x0
I− {x0}
f(x)−f(x0)
x−x0
•f x0f
f x0
f0(x0)
f0(x0) = lim
x→0
f(x)−f(x0)
x−x0

f x0x0
(x)
∀x∈I
(x) = f(x)−f(x0)
x−x0−f0(x0)
f(x) = f(x0) + f0(x0)(x−x0)+(x−x0)(x)
lim
x→x0
(x) = 0
y=f(x0) + f0(x0)(x−x0)
f x0