Page 20 - Math SL HB Sem 2

Maxima, minima and inflection point

/'undclined

f=o
lf)
<o
l'>i 0 /'< 0
h ,l'< 0
i,*fL!h"" I Locrl rnin Lolal min
I'> ll iodrn+ li'=o
i'
I

Critical point
A critical point for a function/is any value ofx in the domain of/at which
I @ = o or f'(x) does not exist ( f' undefined )

Stationary Points

A stationary point is a point where /'(x) = 0. tt could be a local maximum,
local minimum or a horizontal inflection.

horizontal
inflection
Local maximum

-2 l

: \ loceliminimum

On this curve there are three stationary points:
A - is called local maximum and the gradient of the curve is changing from
positive to negative.
B - is called local minimum and the gradient of the curve is changing from
negative to positive.
C - is called point of inflection and the gradient is not changing in sign.