a) 2(y^2-2)=6
solve for y.
y^2-2=6
y= +-sqrt8, x=2
b) y^2+2yy'x-2xy-y'x^2=0
y'(2xy-x^2)=2xy-y^2
y'= you finish it.
c. slope=y', put in the two points in a), and calculate
Consider the equation xy2 − x2y = 6.
(a) Find all points on the graph when x = 2.
(b) Find a formula for dy
dx in terms of x and y.
(c) Find the tangent lines for the points you found in the first part
2 answers
(a) x=2
2y^2-4y = 6
y^2-2y-3 = 0
(y-3)(y+1) = 0
So, the points are (2,3) and (2,-1)
(b)
xy^2-x^2y = 6
y^2 + 2xyy' - 2xy - x^2y' = 0
y'(2xy-x^2) = 2xy-y^2
y' = (2xy-y^2)/(2xy-x^2)
(c)
y'(2,3) = 3/8
y'(2,-1) = 5/8
check:
http://www.wolframalpha.com/input/?i=plot+xy%5E2-x%5E2y%3D6,+y%3D(3%2F8)(x-2)%2B3,+y%3D(5%2F8)(x-2)-1,x%3D2
2y^2-4y = 6
y^2-2y-3 = 0
(y-3)(y+1) = 0
So, the points are (2,3) and (2,-1)
(b)
xy^2-x^2y = 6
y^2 + 2xyy' - 2xy - x^2y' = 0
y'(2xy-x^2) = 2xy-y^2
y' = (2xy-y^2)/(2xy-x^2)
(c)
y'(2,3) = 3/8
y'(2,-1) = 5/8
check:
http://www.wolframalpha.com/input/?i=plot+xy%5E2-x%5E2y%3D6,+y%3D(3%2F8)(x-2)%2B3,+y%3D(5%2F8)(x-2)-1,x%3D2
0 answers