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Would someone please explain how to find the inflection point, y"=0, of the equation y"= 2[4x^315x^2+12x5]/(1x^2)^3 without a graphing calculator, please?
 one year ago
 one year ago
Would someone please explain how to find the inflection point, y"=0, of the equation y"= 2[4x^315x^2+12x5]/(1x^2)^3 without a graphing calculator, please?
 one year ago
 one year ago

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ShiniBest ResponseYou've already chosen the best response.0
You already have the second derivative of the function so all you have to do is set the equation equal to 0 and then solve it. This will give you possible points of inflexion. Then you check the concavity of the point found by substituting the xvalues one higher then the xvalue you found and one lower. If you get a positive on one side and a negative on the other (doesn't matter which) you have found a point of inflexion.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
so is it like this? \[0=\frac{ 2\left[ 4\chi ^{3}15\chi ^{2}+12\chi 5 \right] }{ \left( 1\chi ^{2} \right)^{3} }\] But how do you start to solve it?
 one year ago

ShiniBest ResponseYou've already chosen the best response.0
\[2[4x^3 15x^2 + 12x  5] = 0\] \[4x^3  15x^2 + 12x 5 = 0\] Then solve it from there
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
okay so I got: \[\chi \left( 4\chi ^{2}15\chi +12 \right)=5\] then I used the \[\frac{ b \pm \sqrt{b ^{2}4ac} }{ 2a }\] and got 2.593070331 and 1.156929669. So do I put those numbers in the equation and test if they equal to 0?
 one year ago

ShiniBest ResponseYou've already chosen the best response.0
There is also the value of x = 5. When you used the quadratic formulas to find the xvalues did you first separate the equation you got into: \[x = 5, 4x^2  15x + 12 = 5\] If not, try that. Were you given the original equation? If you were you substitute the values you got into that to get the possible points. If not don't worry. After that i usually check if the concavity changes by drawing: dw:1358129096454:dw and then repeat that for the rest of the x values you got. Sorry im not being a great deal of help anymore, if anything im confusing you more.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
the original equation was \[y =\frac{ 2\chi ^{2}4\chi +3 }{ 1\chi^{2} }\] and I got, When X=4 Y=0.21007 When X=6 Y= 0.05133
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
I still can't find the inflection point...
 one year ago

wioBest ResponseYou've already chosen the best response.1
Since you have an equation of degree 3, you need to find one of the roots first without the help of the quadratic equation.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
The there is another way to find it?
 one year ago

wioBest ResponseYou've already chosen the best response.1
Well you sort of have to guess.
 one year ago

wioBest ResponseYou've already chosen the best response.1
What is the equation we want to find the roots of exactly?
 one year ago

wioBest ResponseYou've already chosen the best response.1
Which function exactly is \(y''\). I see a lot of functions here.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
sorry about that... the first one equation in the question is y". I need to find the inflection point for y"=0
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
\[y"=\frac{ 2\left[ 4\chi ^{3}15\chi ^{2}+12\chi 5 \right] }{ \left( 1\chi ^{2} \right)^{3} }\] to be exact
 one year ago

wioBest ResponseYou've already chosen the best response.1
First thing to notice is that it's undefined at 1 and 1. Next thing to notice is that if the numerator (part on top) is 0, then the whole thing is 0. So we can ignore the denominator as long as we keep the first thing in mind.
 one year ago

wioBest ResponseYou've already chosen the best response.1
I'd start by just distributing that \(2\). There's not reason to have that factored out.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
oh okay... so it's only the \[2\left[ 4\chi ^{3}15\chi ^{2}+12\chi 5 \right]\] part I work with right?
 one year ago

wioBest ResponseYou've already chosen the best response.1
Yes. Ultimately we could multiply both sides by the denominator, and since the other size is 0, it would remain 0.
 one year ago

wioBest ResponseYou've already chosen the best response.1
I suppose you could get rid of that \(2\) with the same logic.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
\[4\chi^{3}15\chi ^{2}+12\chi 5\] is not factorable right?
 one year ago

wioBest ResponseYou've already chosen the best response.1
why is there a negative in front of the 4?
 one year ago

wioBest ResponseYou've already chosen the best response.1
yeah apparently it has a really nasty real root, and two imaginary roots.
 one year ago

wioBest ResponseYou've already chosen the best response.1
Did they give you y'' or y originally?
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
they gave me y originally and I was suppose to sketch the graph and find the inflection points without a graphing calculator
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
\[y=\frac{ 2\chi ^{2}4\chi +3 }{1\chi ^{2} }\]
 one year ago

wioBest ResponseYou've already chosen the best response.1
Why were you opposed to just graphing it?
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
\[y'=\frac{ 4\chi ^{2}+10\chi 4 }{ \left( 1\chi ^{2} \right)^{2} }\]
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
you mean graph it with a calculator or by hand?
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
I have to label the inflection points and I can't find the y"=0 one
 one year ago

wioBest ResponseYou've already chosen the best response.1
The only way to really find it is to use the very erudite formula for 3rd degree polynomials, or use some other root finding method.... like Newton's method.
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
I don't know the other methods....
 one year ago

wioBest ResponseYou've already chosen the best response.1
http://en.wikipedia.org/wiki/Cubic_function#General_formula_of_roots The formula is HUGE
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
I'm not sure if i can memorize that....
 one year ago

wioBest ResponseYou've already chosen the best response.1
Seems like the only thing you could really do is to
 one year ago

wioBest ResponseYou've already chosen the best response.1
graph it and then plug in points really close to the inflection point
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
oh okay... so I can just guess the inflection point then, right?
 one year ago

wioBest ResponseYou've already chosen the best response.1
yeah. The problem seems kinda messed up.
 one year ago

wioBest ResponseYou've already chosen the best response.1
You can sort of see how the tangent line would intersect between 2 and 3
 one year ago

bluebirdBest ResponseYou've already chosen the best response.0
Okay, thank you so much for your help!
 one year ago
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