Question

f(x)=(x^3)/(x^2-4)
Finding local min and max.

Answer 1

I did f '(x)=0 and found 3 solutions:
\[x=0, x=\sqrt{12}, x=-\sqrt{12}\]
Now how do I tell which point is a maximum and which is minimum?

Answer 2

one way is find the second derivative and plug in the values

Answer 3

if f" is positive you ave a minimum, negative is maximum

Answer 4

those answers look good to me
now don't forget you actually know what this looks like from your pre calculus course
thank about all that time you spent with rational functions

Answer 5

or you can use the @cwrw238 way of finding the second derivative, but it will not be too pleasant as your first derivative is complicated enough

Answer 6

yea thats true

Answer 7

also pay attention to the fact that your function is ODD

Answer 8

I've actually found the 2nd derivative and got:
f''(sqrt12)=1.299
f''(-sqrt12)= -1.299

Answer 9

So the first one is a minimum and the second one is a maximum?

Answer 10

yes

Answer 11

i guess what i am trying to say it, don't just use the tools from calculus to analyze the graph of the function,. but rather bring to the problem all you know already

Answer 12

what about f"(0) ?

Answer 13

got a 0, I think it's that point where it switches (forgot the correct term)

Answer 14

Inflection?

Answer 15

yes - a point of inflection

Answer 16

Can i tell at this point which side is concave and which is convex?

Answer 17

- to be honest - i can't recall

Answer 18

Alright, thanks a bunch for the help.
Much appreciated :)

Answer 19

yw