Asked by Stephanie
the curve: (x)(y^2)-(x^3)(y)=6
(dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3))
a) find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points
b)find the x-coordinate of each point on the curve where the tangent line is vertical
(dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3))
a) find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points
b)find the x-coordinate of each point on the curve where the tangent line is vertical
Answers
Answered by
drwls
a) If x = 1, y^2 -y -6 = 0
(y-3)(y+2) - 0
y = 3 or -2
b) Find the points where dy/dx = infinity
Those would be the places where the denominator of dy/dx = 0. x=0 is one such point. Any point where x^2 = 2y would be another, if there is such a point on the curve.
(y-3)(y+2) - 0
y = 3 or -2
b) Find the points where dy/dx = infinity
Those would be the places where the denominator of dy/dx = 0. x=0 is one such point. Any point where x^2 = 2y would be another, if there is such a point on the curve.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.