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IsTim
 4 years ago
how to graph g(x)=3x^4=3x^2
IsTim
 4 years ago
how to graph g(x)=3x^4=3x^2

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IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0I'm looking thru my old notes now, but I can't find anything that could help.

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0I simplified the equation so: g(x)=3x^2(x^2+1)

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0I was thinking apq, but I don't know if that applies to this.

sasogeek
 4 years ago
Best ResponseYou've already chosen the best response.0why do u have 2 equal signs to one function?

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0\[g(x)=3x ^{4}3x ^{2}\] If you want a cleaner version.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.03x^2(x^21) you plug in points frankly :/ it looks like a x^2 graph.

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0So I just plug in values? That's feels "brute". There's no other way?

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0@ Mario; I'm studying for an exam. I don't get those.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0we get to use graph calcs on my exams

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0plug in pounts. their are zeroes at 0, 1,1.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the rest is just brute force plugging. yes. that's how it works.

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0Oh well. I was looking for some equation rearranging. Would that work?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yet i still did poorly lol

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0IF possible, please give an explaination of how to dervie the graph from teh equatioon.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Ok. If g(x)=3x^43x^2 first we'd like to know the zero; i.e., the intercepts on the xaxis. Setting g(x) = 0, we have \[ 3x^2(x^2  1) = 0 \] Hence \[ x = 0, \pm 1 \] Next, what's the yintercept: y = g(0) = 0. Next, critical values ...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1\[ g'(x) = 12x^3  6x = 0 \] if and only if \[ 6x(2x^2  1) = 0 \] i.e., \[ x = 0, \pm 1/\sqrt{2} \] The second derivative is \[ g''(x) = 36x^2  6 = 6(6x^2  1) \] ...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1It's not hard now to show that x = 0 must be a local max and \[ x = \pm 1/\sqrt{2} \] are local mins. So now we have the behavior of the function in the interval [1,1] What happens outside that?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1The next thing we observe is that g(x) is an even function, g(x) = g(x) meaning the function is symmetric about the yaxis. As \[ g(x) = 3x^2(x^2  1) \] it is clear that for \( x > 1 \), \( g(x) > 0 \) and as \( x \rightarrow \infty \), \( g(x) \rightarrow \infty \). We now have all the information we need to draw the graph and it's consistent with the picture I posted above. Make sense?

IsTim
 4 years ago
Best ResponseYou've already chosen the best response.0It's higher level information that I don't understand, but I think if I read thru it a bit more, I'll understand. Thank you very much.
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