Hoofdstuk 15 Afgeleiden en Primitiveren (V6 Wis B) Pagina 1 van 12
PARAGRAAF 15.1 : HELLINGEN, BUIGPUNTEN EN TOPPEN
LES 1 : BUIGPUNTEN
DEFINITIES
(1) Buigpunt = { Punt waar de helling maximaal of minimaal is }
(2) Buigpunt berekenen ⇔ 𝑓𝑓’(𝑥𝑥) heeft een top ⇔ 𝑓𝑓’’(𝑥𝑥) = 0
𝑑𝑑𝑑𝑑
(3) = 𝑓𝑓′(𝑥𝑥)
𝑑𝑑𝑑𝑑
𝑑𝑑 𝑑𝑑𝑑𝑑
(4) � � = 𝑓𝑓′′(𝑥𝑥)
𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑
(5) Bij een buigpunt :
1. Is er een top bij 𝑓𝑓’(𝑥𝑥)
Helling is maximaal of minimaal
2. Gaat 𝑓𝑓’’(𝑥𝑥) door de x-as (van + naar – of omgekeerd).
Helling van 𝑓𝑓’(𝑥𝑥) is daar immers nul
VOORBEELD 1
Gegeven is de formule 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 4 + 𝑥𝑥 3 − 31𝑥𝑥 2 − 𝑥𝑥 + 30. Van deze formule zijn op de
volgende pagina de grafieken van 𝑓𝑓(𝑥𝑥), 𝑓𝑓 ′ (𝑥𝑥) 𝑒𝑒𝑒𝑒 𝑓𝑓 ′′ (𝑥𝑥) geschetst.
a. Geef aan waar de buigpunten zitten in alle 3 de grafieken.
Leg uit aan de hand van alle drie de grafieken of ze toenemend/afnemend stijgend/dalend
zijn op
b. Het interval < -3 , -2 >
c. Het interval < 0 , 2 >
, Hoofdstuk 15 Afgeleiden en Primitiveren (V6 Wis B) Pagina 2 van 12
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