Thread: Increasing/decreasing intervals of a function

1. Increasing/decreasing intervals of a function

1 ) Let g(a,b)® R and let x0 Î (a,b).
Match the two lists.

A(x0,g(x0)) is a critical point Bg is decreasing on (a,b) Cg is increasing on (a,b) Dx0 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 x1,x2 Î (a,b),

x1 < x2 Þ g(x1) < g(x2).

D x0 is a critical number.
D g¢(x0)=0
D g¢(x0) does not exist.

2.) For f(x) = x6 /7 -x13 /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

2. Originally Posted by lemontea
1 ) Let g(a,b)® R and let x0 Î (a,b).
Match the two lists.

A(x0,g(x0)) is a critical point Bg is decreasing on (a,b) Cg is increasing on (a,b) Dx0 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 x1,x2 Î (a,b),

x1 < x2 Þ g(x1) < g(x2). answer is C. try to graph by giving some examples..

D x0 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¢(x0)=0 yes..
D g¢(x0) does not exist. yes..

2.) For f(x) = x6 /7 -x13 /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
i don't understand the thing in orange. is it $\displaystyle f(x) = \frac{x_6}{7}-\frac{x_{13}}{7}$?