Increasing/decreasing intervals of a function

**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*).

**B** *g*¢(*x*) < 0 for all *x* Î (*a*,*b*).

**A** For any *x*1,*x*2 Î (*a*,*b*),

*x*1 < *x*2 Þ *g*(*x*1) < *g*(*x*2).

**D** *x*0 is a critical number.

**D** *g*¢(*x*0)=0

**D** *g*¢(*x*0) does not exist.

**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:)