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anonymous
 one year ago
more implicit differentials
for what values of x does the curve y^2 x^4 + 2xy 18x^2 = 10 have vertical tangent lines?
anonymous
 one year ago
more implicit differentials for what values of x does the curve y^2 x^4 + 2xy 18x^2 = 10 have vertical tangent lines?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @IrishBoy123 any ideas?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Horizontal tangent lines when: \(\large\rm y'=0\) Vertical tangent lines when: \(\large\rm y'=\frac{stuff}{0}\) Have you tried finding your y' yet? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i feel i messed up somewhere though so im redoing that right now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im getting \[y'= \frac{ 4x(x^2+9) }{ 2(y+x) }\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Hmm I think there is another term on top. Did you forget to product rule again? :)\[\large\rm y^2 x^4 + \color{orangered}{2xy} 18x^2 = 10\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no i just simplified from 4x^3 + 36x

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3But where is the 2y in the numerator? :o hmm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh your totally right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0argh your so clever :P

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm y^2 x^4 + 2xy 18x^2 = 10\]Differentiating gives,\[\large\rm 2yy'4x^3+2y+2xy'36x=0\]That's your first step ya? :D

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3you're* that's gonna bug me, i had to lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah i even crossed it out and all i guess it just slipped my mind when i was rewriting it on the other side of the equal sign

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyway so its \[y'= \frac{ 4x^3 + 36x + 2y }{ 2(x+y) }\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Woops, 2y on top I think ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Anyway, let's just get rid of all the 2's I guess,\[\large\rm y'=\frac{2x^3+18xy}{x+y}\]That's the only simplification that really cleans it up nicely.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:( yes , okay so now what?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3This derivative function is undefined when the denominator is zero. (This is also when we're getting vertical tangents.)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3So vertical tangent when the denominator is zero, \(\large\rm x+y=0\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Overheat again? :) LOL

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441787497363:dw where its undefined? :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep :( i need a new computer

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Hmm ya that's a weird answer :o I do something wrong?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyway one of the answer choices is x = y so i think that's the answer right?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3yay team \c:/ it just doesn't make a whole lot of sense with the graph of the function :D I guess I just need to think about it a sec lol

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0I think that's about right, it's either \(\sf y=x\) or \(\sf x=y\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you once more :D
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