Find all vertical tangent lines of a curve - more than one variable

In summary, to find all vertical tangent lines of the curve xy^2 - x^3y = 6, we can use implicit differentiation and set the derivative equation (3x^2y - y^2) / (2xy - x^3) equal to 0 to find the x coordinates of points where the tangent line is vertical. However, if there are any errors in the process, it is recommended to refer to the course book or show the steps taken for assistance.
  • #1
mwilks
1
0
find all vertical tangent lines of a curve - more than one variable!

curve : xy^2 - x^3y = 6
derivative : (3x^2y - y^2) / (2xy - x^3)
question : find the x coordinate of each point on the curve where the tangent line is vertical.

after some consideration, i decided that when the derivative equation is underfined, the tangent line is vertical. so, 2xy-x^3=0. was that right? now what?
 
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  • #2


How did you arrive at that "derivative"?
 
  • #3


Look up implicit differentiation in your course book. Seems you tried to do it but made some error on the way. Try showing your steps to us.
 

FAQ: Find all vertical tangent lines of a curve - more than one variable

What is a vertical tangent line?

A vertical tangent line is a line that is perpendicular to the curve at a specific point and has an undefined slope. This means that the line is parallel to the y-axis and does not have a defined slope value.

How do you find the vertical tangent lines of a curve?

To find the vertical tangent lines of a curve, you must first take the derivative of the curve. Then, set the derivative equal to zero and solve for the variable. The values of the variable that make the derivative equal to zero will be the x-coordinates of the points where there are vertical tangent lines.

Can there be more than one vertical tangent line for a curve?

Yes, there can be multiple vertical tangent lines for a curve. This can occur when the curve has sharp turns or cusps. In these cases, the derivative may equal zero at multiple points, resulting in multiple vertical tangent lines.

What is the significance of finding the vertical tangent lines of a curve?

Finding the vertical tangent lines of a curve can provide valuable information about the behavior of the curve. It can help identify any sharp turns or cusps, and can also be used to determine the maximum and minimum values of the curve.

Can vertical tangent lines exist for curves in more than one variable?

Yes, vertical tangent lines can exist for curves in more than one variable. In this case, the derivative would be taken with respect to one variable while keeping the other variables constant. The resulting values would indicate the points where there are vertical tangent lines in the curve.

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