The discussion revolves around finding the equation of the tangent line at the point (2,2) for the implicit function defined by f(x)=xy+y^3=12. Participants are exploring the process of determining the slope of the tangent line and how to correctly formulate the equation based on that slope.
Some participants have identified potential errors in their calculations, particularly regarding the formulation of the tangent line equation. There is an ongoing exploration of the implications of these errors, with suggestions to clarify the steps taken in deriving the equations.
There is a noted confusion regarding the correct application of the point-slope form of the line equation and how it relates to the calculated slope. Participants are also reflecting on the importance of ensuring that the tangent line passes through the specified point (2,2).
1MileCrash said:Homework Statement
Find the equation for the tangent line at (2,2)
f(x)=xy+y^3=12
Homework Equations
The Attempt at a Solution
I really feel like I know what I'm doing here, but the key disagrees.
My equation for the tangent slope comes out to be:
(-y)/(x+3y^2)
when solved for my (2,2), I get a slope of -1/7
Yielding an entire equation of y= -1/7x + 12/7
1MileCrash said:If my slope is correct, but my tangent line equation is wrong, I can only assume I did something wrong in y - y = M(x-x)?
1MileCrash said:I used y - 2 = M (x - 2), y = 2 and x = 2.
What else could I have used? I think I'm getting confused..
1MileCrash said:Ahh, I think I see now, a sign error?
y - 2 = -1/7x + 2/7
y = -1/7x + 16/7
Dick said:Yes. Sign error. Looks ok now. If you'd post all of your work to begin with it would be easier to diagnose these things.
1MileCrash said:Sorry about that, but thanks for the help!