**1 ) **Let

*g(**a*,

*b*)

® *R* and let

*x*0

Î (

*a*,

*b*).

Match the two lists.

A(

*x*0,

*g*(

*x*0)) is a critical point B

*g* is decreasing on (

*a*,

*b*) C

*g* is increasing on (

*a*,

*b*) D

*x*0 is a critical number

**C** g¢(

*x*) > 0 for all

*x* Î (

*a*,

*b*).

yes.. **B** *g*¢(

*x*) < 0 for all

*x* Î (

*a*,

*b*).

yes.. **A** For any

*x*1,

*x*2

Î (

*a*,

*b*),

*x*1 <

*x*2

Þ *g*(

*x*1) <

*g*(

*x*2).

answer is C. try to graph by giving some examples.. **D** *x*0 is a critical number.

i say A. (of course, one would choose D but see, D is just a re-statement of the question.) **D** *g*¢(

*x*0)=0

yes.. **D** *g*¢(

*x*0) does not exist.

yes.. **2.) **For

*f*(*x*) = *x*6 /7 -*x*13 /7 find the critical numbers and open intervals where the function is increasing and decreasing.

**Solution:**
Since

*f*¢(

*x*)= ____________

,we see that

*f*¢(

*x*)=0 if

*x*= __________ and that

*f*¢( __________ ) does not exist.

Therefore, the critical numbers are __________ and __________ .

is increasing on an interval if

*f*¢(

*x*) > for each

*x* on that interval. Therefore the given function is increasing on the interval ( __________ , __________ ).

*f* is decreasing on an interval if

*f*¢(

*x*) < for each

*x* on that interval. Therefore the given function is decreasing on (

- ¥, __________ )

È( __________ ,

¥).

The text in red is the answers i got..but there is something wrong with it...can someone help me...and there are two questions where i am completely clueless ...can anyone help! appreciate it