Posted by Fredrick E. on Tuesday, November 1, 2011 at 2:35pm.
find all points on the curve x^2y^2+xy=2 where the slope of the tangent line is 1
I know that you have to find the derivative when it equals 1
i got
y'=(2x*y^2y)/(2x^2*y+x)
(i don't know if it is correct or not)
but i don't know how to go from here. any help would be good
Thanks

calculus  bobpursley, Tuesday, November 1, 2011 at 3:21pm
try changing variables. let z=xy in the origianal equation, solve for z
z^2+z2=0
(z+2)(z1)=0
z=1 or 2 or z is a constant.
Then z=xy or
z'=y+xy'=0
but y'=1
y=x and xy=1 or 1
xy=x^2
2=x^2
x=sqrt2, y=x =sqrt2
check: original line 42=2 checks.
1=x^2
x=i, y=x=i
check: originalline 1=1=2 checks.
solutions:
pointA: x=i,y=1
PointB: x=sqrt2, y=sqrt2

calculus  Anonymous, Tuesday, November 1, 2011 at 6:44pm
Can you explain using implicit differention?

calculus  bobpursley, Tuesday, November 1, 2011 at 10:07pm
No, I tried it that way, it bogged down in a third degree equation after I substituted, so I gave up that way.
Answer This Question
Related Questions
 calculus  find all points on the curve x^2y^2+xy=2 where the slope of the ...
 Calculus  Tangent Line  Hi, im having problems with the following problem. The...
 Calculus  I have a two part question that pertains to a curve (r(x)) and its ...
 calculus  Find all points on the curve x^2y^2+xy=2 where the slope of tangent ...
 Calculus  Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...
 Calculus  Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2yx...
 12th Grade Calculus  1. a.) Find an equation for the line perpendicular to the ...
 calculus  1. Given the curve a. Find an expression for the slope of the curve ...
 Ap Calc AB  Find the equation of the line tangent to the curve at (5, 3) (x2...
 calculus  1. Which of the following expressions is the definition of the ...
More Related Questions