3.1 Maximum and Minimums
Def: Let c be in the domain, 0, of a function, f. Then, c) is
Example:
the
'
•Absolute ugrimum value of f on O if texts cs for
X in
Oif fcc)
•Absolute minimum value off on Dit for a fee) for
A
Def. Suppose
x in
са
Then, cs is
of
y=f(x) t has an absolute
open
a
max
ut
x=2
abs dute max of
Fla₂)
عام
I has on aks. min at xxc;.
The abs min. is at ccy
Local mins @ x=ci.
Local max@x=C1, C2
internet, I, carfutning c, is within the doncie D off.
Locat maximum value off if f(x) s fee) for all x in I
: Local minimum value of f if fox) fcc) for all x in I
* Local extreme will never occur at end points
example: Find the abs./local extrenca of fors=(x-2)=3
a) (0, 31
over the speci ed intervals Comarcal
Abs Maxi 3. Local max: 3.
Abs Min: DNE Local mini Mars
fi fi fi fi fi
Def: Let c be in the domain, 0, of a function, f. Then, c) is
Example:
the
'
•Absolute ugrimum value of f on O if texts cs for
X in
Oif fcc)
•Absolute minimum value off on Dit for a fee) for
A
Def. Suppose
x in
са
Then, cs is
of
y=f(x) t has an absolute
open
a
max
ut
x=2
abs dute max of
Fla₂)
عام
I has on aks. min at xxc;.
The abs min. is at ccy
Local mins @ x=ci.
Local max@x=C1, C2
internet, I, carfutning c, is within the doncie D off.
Locat maximum value off if f(x) s fee) for all x in I
: Local minimum value of f if fox) fcc) for all x in I
* Local extreme will never occur at end points
example: Find the abs./local extrenca of fors=(x-2)=3
a) (0, 31
over the speci ed intervals Comarcal
Abs Maxi 3. Local max: 3.
Abs Min: DNE Local mini Mars
fi fi fi fi fi
