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\[-2[4x^3 -15x^2 + 12x - 5] = 0\]
\[4x^3 - 15x^2 + 12x -5 = 0\]
Then solve it from there

I mean Y" oops.

I still can't find the inflection point...

Ummm
still need help?

The there is another way to find it?

*then

Well you sort of have to guess.

What is the equation we want to find the roots of exactly?

Which function exactly is \(y''\). I see a lot of functions here.

Um ok still here?

I'd start by just distributing that \(-2\). There's not reason to have that factored out.

I suppose you could get rid of that \(-2\) with the same logic.

\[-4\chi^{3}-15\chi ^{2}+12\chi -5\] is not factor-able right?

why is there a negative in front of the 4?

oh oops i mean 4

yeah apparently it has a really nasty real root, and two imaginary roots.

Did they give you y'' or y originally?

What was y?

\[y=\frac{ 2\chi ^{2}-4\chi +3 }{1-\chi ^{2} }\]

Oh wow, what was y'?

Why were you opposed to just graphing it?

\[y'=\frac{ -4\chi ^{2}+10\chi -4 }{ \left( 1-\chi ^{2} \right)^{2} }\]

you mean graph it with a calculator or by hand?

by hand

I have to label the inflection points and I can't find the y"=0 one

or bisection

I don't know the other methods....

http://en.wikipedia.org/wiki/Cubic_function#General_formula_of_roots
The formula is HUGE

I'm not sure if i can memorize that....

Seems like the only thing you could really do is to

graph it and then plug in points really close to the inflection point

oh okay... so I can just guess the inflection point then, right?

yeah. The problem seems kinda messed up.

You can sort of see how the tangent line would intersect between 2 and 3

Okay, thank you so much for your help!