1

Exampie;

The

total

gost

function

for

a

gveu

business

is

given

by

C(x)

=

*L

tSd*

gx

r50.

The

domain

for

the

number

ofunits

(.x)

of

the item produced

is I

s x

<

donlv.

Find

the

maximum

and

minimum

costs

that

this

business

will

face.

l**tpt.Z,;it&eeu

ttlCq

.f '/*,)

=o

a*,0

.* its

t

,

k=

6

C?x)=

gXL-Soxtlt:c

*

*2-ro**/6=a

-+

(x-?)(**z)ao

-+

l(.*tr*Fe..

Crr(z)

<O +rr.Ara

,

Ctr'ts?4

(Ut.AJ4

)

c

crl

=

?4

,

c(

r.t

=

t*

(uazh,&-)

"il*l

A4t

at

xez

+

Ct')=?+

liu;

e4t

,rf

rc,=b

t ect

)=

t4

sllfrl-

"

lAt*c

illal

?e

E";

taaJ

16rt4)

Example:

Find

the

absolute

{gilobal)

maximum

and

the

absolute

minimum

values

for

the

ftnction

(*)

=

Zx'-*'-

20*

+

40

over

the

closed

interval

[-2;5].

ruv

^sv&'Ivr

{/x\,

621

lr-2Q=a

-+

7xt-

*,-ta=e

+

(Sz+r)(r-l);o

-t

)L

s

-f

,7

=Z

.

Ofur#

A44'HJ<

z

=

-2,

L=

{

ht/-.,,;-

f,/x)

t*

S=

a-'rt

f

*t*fr'*z-'*

6*

n-1h*ce-,

{

C-

r/)

x

6

l,

3o,

{rz)=

t:.1

{t-z)

c

6o, *(t)=

13f,

d

*=

d

+

*(s)=

tO{

a* 2?2

'+

JF(a)s

re'

fir-

S/aaL

7r4L

t

G

fo;

aoaJ

?/ltx

?/t;

xebz;s7.