f'(x) = -2x / (3x-1)^3

Can someone tell me why 0 is a critical point of this? I can see when 1/3 is, but I don't understand why 0 also is. Test tomorrow need to learn!

Question

f'(x) = -2x / (3x-1)^3

Can someone tell me why 0 is a critical point of this? I can see when 1/3 is, but I don't understand why 0 also is. Test tomorrow need to learn!

fibonaccichick666 · Answer

So, what has to happen for something to be a critical point?

fibonaccichick666 · Answer

like, can you define critical point?

anonymous · Answer

Uhhhh where a function is either undefined, a local min or max, or an absolute min or max? That's probably a bad definition as I know all critical points don't have to be local or abs min/max but that's my best shot hahahah.

anonymous · Answer

Solutions to x=0 for the first derivative?

fibonaccichick666 · Answer

that's ok, now, what happens to the derivative when you have any min max?

anonymous · Answer

Changes signs as slope will be going from - to + or + to -

fibonaccichick666 · Answer

ok, and when we go from positive to negative or vice versa we have to pass which point?

fibonaccichick666 · Answer

y=?

anonymous · Answer

0!

fibonaccichick666 · Answer

yea, so better definition of a critical point is any time the first derivative =0.  That means we change direction potentially.  Now, in your problem, what does x have to equal to make the numerator =0?

fibonaccichick666 · Answer

and also where it is undefined**

anonymous · Answer

Ohhhh okay so the 0 comes from the numerator?

fibonaccichick666 · Answer

yea, so remember a fraction equals zero if the numerator =0

anonymous · Answer

So if I got a numerator where equaling it to 0 was a number other than 0 it would be a critical point

fibonaccichick666 · Answer

so just keep in mind, find all zeroes and underfined points of the 1st deriv. oh, and watch this video. It will make you happy https://www.youtube.com/watch?v=uqwC41RDPyg

fibonaccichick666 · Answer

So long as the denominator is not zero as well, yes.

anonymous · Answer

Awesome thanks for the help! I'll surely have more questions if ya want more calc fun tonight look around for them hahaha

fibonaccichick666 · Answer

haha, maybe, but watch the video, it's actually a great review.  Put closed captions on.

fibonaccichick666 · Answer

and np

anonymous · Answer

Would 1/(3x-1)^3   just have the critical point at 1/3?

fibonaccichick666 · Answer

yep

anonymous · Answer

Kk awesome! Got it

fibonaccichick666 · Answer

with uhh, I can't think of the wordddddddd sorry, but it's called like a zero of order 3 or something

fibonaccichick666 · Answer

here, you said you have a test tomorrow?

anonymous · Answer

Sir yes sir

fibonaccichick666 · Answer

what school/level?

anonymous · Answer

UGA calc 1

fibonaccichick666 · Answer

I can get you some practice exams

anonymous · Answer

I have one! Doing it now :)

fibonaccichick666 · Answer

http://examswithsolutions.com/Subjects/math_exams.html

anonymous · Answer

Awesome that looks like a great tool!

fibonaccichick666 · Answer

you can always use this little trick google "  site: .edu calculus 1 exam "

fibonaccichick666 · Answer

then use paul's online notes for quick reference

anonymous · Answer

Thanks a ton my dude :)

fibonaccichick666 · Answer

np, you gotta understand, math major who was put through this crud.  I sympathize.  good luck, shoot a dew and some sour patch kids 10 minutes before the exam :)

anonymous · Answer

Hahahah will do just for you! Need all the luck I can get, awful at math and this is the last math class I'll ever need!

fibonaccichick666 · Answer

well, it actually helps because of the combined caffienne and sugar high, you can do it, just keep telling yourself that