anonymous
  • anonymous
more implicit differentials for what values of x does the curve y^2 -x^4 + 2xy -18x^2 = 10 have vertical tangent lines?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@ganeshie8 @IrishBoy123 any ideas?
zepdrix
  • zepdrix
Horizontal 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
  • anonymous
yes

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anonymous
  • anonymous
i feel i messed up somewhere though so im redoing that right now
anonymous
  • anonymous
im getting \[y'= \frac{ 4x(x^2+9) }{ 2(y+x) }\]
zepdrix
  • zepdrix
Hmm 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
  • anonymous
no i just simplified from 4x^3 + 36x
zepdrix
  • zepdrix
But where is the -2y in the numerator? :o hmm
anonymous
  • anonymous
oh your totally right
anonymous
  • anonymous
argh your so clever :P
zepdrix
  • zepdrix
\[\large\rm y^2 -x^4 + 2xy -18x^2 = 10\]Differentiating gives,\[\large\rm 2yy'-4x^3+2y+2xy'-36x=0\]That's your first step ya? :D
zepdrix
  • zepdrix
you're* that's gonna bug me, i had to lol
anonymous
  • anonymous
yeah 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
  • anonymous
anyway so its \[y'= \frac{ 4x^3 + 36x + 2y }{ 2(x+y) }\]
zepdrix
  • zepdrix
Woops, -2y on top I think ya?
zepdrix
  • zepdrix
Anyway, let's just get rid of all the 2's I guess,\[\large\rm y'=\frac{2x^3+18x-y}{x+y}\]That's the only simplification that really cleans it up nicely.
anonymous
  • anonymous
:( yes , okay so now what?
zepdrix
  • zepdrix
This derivative function is undefined when the denominator is zero. (This is also when we're getting vertical tangents.)
zepdrix
  • zepdrix
So vertical tangent when the denominator is zero, \(\large\rm x+y=0\)
zepdrix
  • zepdrix
Overheat again? :) LOL
Jhannybean
  • Jhannybean
|dw:1441787497363:dw| where its undefined? :P
anonymous
  • anonymous
yep :( i need a new computer
zepdrix
  • zepdrix
Hmm ya that's a weird answer :o I do something wrong?
anonymous
  • anonymous
anyway one of the answer choices is x = -y so i think that's the answer right?
zepdrix
  • zepdrix
yay 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
  • Jhannybean
I think that's about right, it's either \(\sf y=-x\) or \(\sf x=-y\).
anonymous
  • anonymous
thank you once more :D

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