- #1

Schaus

- 118

- 5

## Homework Statement

Find the equation of the tangent line to the curve ##\ xy^2 + \frac 2 y = 4## at the point (2,1).

Answer says ##\ y-1 = -\frac 1 2(x-2)##

And with implicit differentiation I should have gotten ##\frac {dy} {dx}= -\frac {y^2} {2xy-\frac {2} {y^2}}##

## Homework Equations

##\ y-y_1 = m(x-x_1)##

## The Attempt at a Solution

##\ y-1 = m(x-2)##

##\frac d {dx}(xy^2+\frac 2 y) =\frac d {dx}(4)##

##\frac d {dx}(xy^2)+\frac d {dx}(\frac 2 y) = 0##

##2xy+x⋅\frac {dy} {dx}-\frac {2} {y^2}⋅ \frac {dy} {dx} = 0##

##x⋅\frac {dy} {dx}-\frac {2} {y^2}⋅ \frac {dy} {dx} = 2xy##

##\frac {dy} {dx}(x-\frac {2} {y^2})= 2xy##

##\frac {dy} {dx}= -\frac {2xy} {x-\frac {2} {y^2}}##

Subbing in my x and y values gives me a slope of 4.

If anyone can help show me what I did wrong, I would really appreciate it. Also this is the first time using LaTeX Primer so bare with me.