S K R I P T 2 0 1 9

Mathe für die BRP zentral
IV Analysis
Beispiele:
3
f (x) =
f ’ (x) = 0
2
f (x) =
f ’ (x) = 0
f (x) = a 3 f ’ (x) = 0
f (a) = a 3 f ’ (a) = 3 a 2
Beispiel: Gegeben ist die Funktion y = a⋅b2 ⋅x
c
– Ermittle f ′ (a), f ′ (b), f ′ (x), f ′ (c)
f(a) = a⋅b2 ⋅x
c
f(b) = a⋅b2 ⋅x
c
f(x) = a⋅b2 ⋅x
c
f(c) = a⋅b2 ⋅x
c
→ f ′ (a) = 1⋅a0 ⋅ b 2 ⋅x
→ f ′ (b) = a⋅2⋅b1 ⋅x
→ f ′ (x) = a⋅ b2 ⋅1⋅x 0
c
c
c
= 1⋅b2 ⋅x
c
= 2⋅a⋅b⋅x
c
= a⋅b2 ⋅1
c
= a ⋅ b 2 ⋅ x ⋅ c −1 → f ′ (c) = a ⋅ b 2 ⋅ x ⋅ (−1) ⋅ c −2 = − a⋅b2 ⋅x
Beispiel: f (x) = 6 x 2 – 4 x + 3 f ’ (x) = 6 . 2 x 1 – 4 . 1 . x 0 + 0 = 12 x – 4
Nur zur Ansicht
Man darf gliedweise ( + – ) getrennt differenzieren.
Beispiele:
f (x)
2
3
x
3
1
4
x
2
1
2 2 1
f '(x) .3. x .2.x – 0 2 x
3 4
2
1
2
x
c 2
f (x) = a x 3 + b x 2 + c x 1 + d
f ’ (x) = a . 3 . x 2 + b . 2 . x + c . 1 . x 0 + 0 = 3 a x 2 + 2 b x + c
manfred.ambach 256 pro-test.at