## 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?

1. anonymous

@ganeshie8 @IrishBoy123 any ideas?

2. 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? :)

3. anonymous

yes

4. anonymous

i feel i messed up somewhere though so im redoing that right now

5. anonymous

im getting $y'= \frac{ 4x(x^2+9) }{ 2(y+x) }$

6. zepdrix

Hmm I think there is another term on top. Did you forget to product rule again? :)$\large\rm y^2 -x^4 + \color{orangered}{2xy} -18x^2 = 10$

7. anonymous

no i just simplified from 4x^3 + 36x

8. zepdrix

But where is the -2y in the numerator? :o hmm

9. anonymous

10. anonymous

11. 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

12. zepdrix

you're* that's gonna bug me, i had to lol

13. 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

14. anonymous

anyway so its $y'= \frac{ 4x^3 + 36x + 2y }{ 2(x+y) }$

15. zepdrix

Woops, -2y on top I think ya?

16. 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.

17. anonymous

:( yes , okay so now what?

18. zepdrix

This derivative function is undefined when the denominator is zero. (This is also when we're getting vertical tangents.)

19. zepdrix

So vertical tangent when the denominator is zero, $$\large\rm x+y=0$$

20. zepdrix

Overheat again? :) LOL

21. Jhannybean

|dw:1441787497363:dw| where its undefined? :P

22. anonymous

yep :( i need a new computer

23. zepdrix

Hmm ya that's a weird answer :o I do something wrong?

24. anonymous

anyway one of the answer choices is x = -y so i think that's the answer right?

25. 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

26. Jhannybean

I think that's about right, it's either $$\sf y=-x$$ or $$\sf x=-y$$.

27. anonymous

thank you once more :D