OK, I think I see your problem, but I'll ask you these questions before I proceed: (1) What function are you differentiating? (2) With respect to which variable are you differentiating it?

YESSIR!!!!???!?!?!

This is the question alone. No more info has been given. I think with respect to r because r0 will be a constant and so will k.

OK, so which function are you differentiating?

v(r) is the one I am differentiating.

Very good. Expand v(r) by multiplying out the terms completely (i.e., $r^2$ by the rest of the equation). Remember that $k, r_0$ are constants.

I did that and got v ' (r) = 2krr0-3k(r^2)

so then I set v'(r) = 0 and got r= -2/3(r0), is this correct so far?

Hey. You shouldn't get r=(-2/3)r_0

hey,

ok y?

your derivative is correct

so then i should set it equal to 0 right?

but you put in a negative sign where you didn't need one

yes

wait so v'(r) is in fact equal to 2krr0-3k(r^2)?

yes

ok i see it, it should be 2/3(r0)

yep

(2/3)(r0)

but there's another value r could also be

actually nvm

k cool

no wait, sorry-

wat

2k(r_0)r=3k(r^2) implies that r=(2/3)r_0 or r=0

so don't forget your zero value

yeah but aren't we just solving for one variable, r?

sure

r0 is a constant like k

that variable can have 2 values

for example, for y=x^2=0, x can be -1 or 1

now that you have your two critical points, r=0 and r=(2/3)r_0, you need to test which one is an absolute maximum

this one is easy to see: plug both into your original function and take the higher of the two

ok let me try this

real quick

ok

k im not sure about the r=0 solution

if we solve for r we get r=(2/3)(k/k)(r0)

ok, literally write out the derivative you showed me

k

oh u mean on here?

sure

2krr0-3k(r^2)

=0

set that equal to zero, and then put one term on each side

without simplifying

2krr0=3k(r^2)

OH CRAP

very good

you see?

SORRY

it's fine

its late man hahaaa

lol

didnt see the extra r

lol

now, is r_0 positive or negative?

+

radius of the tracea when normal

ok, so which interval of r_0 does your problem specify?

***which interval of r, in terms of r_0

um

3/4(r) to 3/2r?

nope

k hold on

(hint: part (a))

hey i really appreciate u doing this by the way

u DA BAWS

no prob

lulz

I lol'ed at your photo, which is why I decided to answer

y?? haa

hey did u just hack my comp

lol

your icon, the king squirrel

i don't hack 8)

holy shit I accidentally opened up a photo of mine right when u said that

thtought u hacked into my comp and said lol at my pic

ha

anyway man i g2g

but anyway

k im lost at this

last step

now that you have two values for r, pick the relevant one

and go from there

so the biggest one will be the max right

?

and i plug it into v'(r)?

you only have to plug one in

again, look at the domain they assign you

oh ok

alright thanks so much man, appreciate that so much

aight man peace

cya