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) 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.
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:)