Question

Find the critical numbers for 8x-12x^(2/3)

Answer 1

To find a critical number you must first find the derivative of the function which is in this case:\[f'(x) = 8 - 8(x)^(-1/3)\]

then you take the 2 conditions for the critical numbers :

1) f'(x) = 0
2) f'(x) is undefined, hence we have Vertical Asymptotes

Answer 2

give it a try now ^_^

Answer 3

8 - (8/cbrt(x))

8cbrt(x) - 8
---------- = 0 : when x = 1
cbrt(x)

x = 1 is a critical number....

But is it a max or min? or even an inflection? test with the second derivative...

Answer 4

If I did it right, its a minimum....

Answer 5

to find the critical points we derive once and to find the inflection points we derive twice ^_^

Answer 6

she just wants to find the critical numbers lol :)

Answer 7

so the one you have found is a critical number :)

Answer 8

actually, there are some instances where an inflection point has a 0 slope, so it is premature to say that y' = 0 is NOT an inflection.

Answer 9

all she wanted was the critical numbers ^_^

Answer 10

yep; and I think its 1 right? if I did it right :)

Answer 11

yes ^_^

Answer 12

whew!! .... :)

Answer 13

:D