implicit differentiation

• Mar 25th 2010, 12:36 PM
FinalFantasy9291
implicit differentiation
umm i don't remember how to find the slope for this problem.

use implicit differentiation to find and equation of the line tangent to the graph at the point (2,0)

e^y + x^2 - 3y^2=5

so i know the tangent formula is (y-y1) = m (x-x1)
• Mar 25th 2010, 12:40 PM
General
Quote:

Originally Posted by FinalFantasy9291
umm i don't remember how to find the slope for this problem.

use implicit differentiation to find and equation of the line tangent to the graph at the point (2,0)

e^y + x^2 - 3y^2=5

so i know the tangent formula is (y-y1) = m (x-x1)

Well,
you have x1 = 2 , y1 = 0 ..

By differentiating both sides w.r.t. x, we got:

$y' e^y + 2x - 6yy' = 0$

solve for y' , then evaluate it at (2,0), i.e. when x=2 and y=0 to get the value of m ..

then substitute x1,y1 and m the tangent line's formula ..

Please, note that its called "tangent line's formula" not "tangent formula" ..
• Mar 25th 2010, 12:47 PM
akilele
..
• Mar 25th 2010, 12:49 PM
FinalFantasy9291
thank you for that correction haha.

so from what you gave me i got (y-0)=-4(x-2) is that correct?
• Mar 25th 2010, 12:51 PM
General
Quote:

Originally Posted by FinalFantasy9291
thank you for that correction haha.

so from what you gave me i got (y-0)=-4(x-2) is that correct?

Let me see your work ..
mayba you have mistakes ..
If you got the right final answer, that does not mean you've solved the problem correctly ..
• Mar 25th 2010, 12:59 PM
FinalFantasy9291
okay so..

y'e^y+2x-6yy' = 0

btw is there a way i can type this out without having to use ^ so it's not as confusing for you or me?

y'e^0+(2)-6(0)y'=0
y' + 4= 0
y'=-4

so... (y-0)=-4(x-2)
• Mar 25th 2010, 01:01 PM
General
Quote:

Originally Posted by FinalFantasy9291
btw is there a way i can type this out without having to use ^ so it's not as confusing for you or me?

Yes. Use the latex.

Quote:

Originally Posted by FinalFantasy9291
o
y'e^0+(2)-6(0)y'=0

I think that 2 is just a typo .. Right?
It should be 4..

Quote:

Originally Posted by FinalFantasy9291
so... (y-0)=-4(x-2)

Correct.
• Mar 25th 2010, 01:31 PM
FinalFantasy9291
hehe. how do i use the latex?

tyvm
• Mar 25th 2010, 01:40 PM
General
Quote:

Originally Posted by FinalFantasy9291
hehe. how do i use the latex?

tyvm

http://www.mathhelpforum.com/math-help/latex-help/