How would I use this optimized equation: V= 4x^3-64x^2+240x to find a max/min? I'm having trouble finding c

Question

anonymous · Answer

you looking for the max and min of V?

anonymous · Answer

Yeah.

anonymous · Answer

calculus class?

anonymous · Answer

Yep. V is the volume of a box

anonymous · Answer

And there is no given interval or anything

anonymous · Answer

take the derivative, set it equal to zero, solve for $x$

anonymous · Answer

it is a cubic polynomial so it goes from $-\infty$ to $\infty$ there will be no global max or min, only local ones

anonymous · Answer

That's where I'm stuck, I got 12x^2-128x+240=0, but I'm having trouble with the rest

anonymous · Answer

get rid of the 12 first

anonymous · Answer

meaning factor it out?

anonymous · Answer

ok i guess 12 does not go in to 128 but 4 does

anonymous · Answer

yeah the roots are ugly, need to use the quadratic formula
that, or cheat

anonymous · Answer

Okay. I divided both sides by 4 (is that okay? because I'm dividing 0 by 4, so I'll lose it forever, right?) and got 3x^2-32x+60=0

anonymous · Answer

OH I forgot about the quadratic formula

anonymous · Answer

no real choices here
you can try to factor all day and you will not find the factors
use the formula

anonymous · Answer

So I'd get a plus/minus something and then I'd plug it into the original equation, and the smaller number would be the min and the larger number would be the max?

anonymous · Answer

oh no you don't need to do that

anonymous · Answer

cubic polynomial, leading coefficient is positive, looks like this |dw:1412212077810:dw|

anonymous · Answer

the smaller of the two roots will be a local max, the larger will be a local min
you know this before you start

anonymous · Answer

Oh okay. Does that work for all critical values, or just for cubic functions?

anonymous · Answer

no not for everything
my guess is you have seen a cubic polynomial so you have a general idea of what they look like
of course 4th degree polynomials look different etc

anonymous · Answer

Okay! In other cases though, I'd plug it into the original, etc. right?

anonymous · Answer

this like one of these "a box is made out of a flat sheet of cardboard..." problems?

anonymous · Answer

Yes!

anonymous · Answer

lol how'd i guess? usually they are cooked up to give nice answers, i guess not in this case

anonymous · Answer

did you start with something like 
$$V(x)=x(8-2x)(12-2x)$$  ?

anonymous · Answer

No, it was V= x(12-2x)(20-2x)

anonymous · Answer

ok so one side was 12 and the other side 20 too bad
this one gives nice ugly answers

anonymous · Answer

Yeah, it is! Anyways, thanks for the help!!

anonymous · Answer

yw

amistre64 · Answer

was this part of a larger question?