1. ## More implicit differentiation.

Here's the problem:

"Consider the curve defined by $\displaystyle y^2+xy+x^2=15$.

a) Calculate dy/dx.

b) Show that at the two points where y=0, the tangent lines at those points are parallel.

c) Find the coordinates of all points at which there is a horizontal tangent line. Show your work."

For dy/dx, I got dy/dx= -(2x-y)/(2y+x). Is this correct?

Also, could someone show me how to do parts b) and c)?

2. On part A it should be $\displaystyle \frac{-(2x+y)}{(2y+x)}$.

For part B they are asking you to show that at the two points where y is equal to 0, that the slopes are parellel. Of course, you need to find out where those two points are. Plugging in y=0 into your equation will show you where those two points are.

For part C, they are asking for the point's where the derivative of your equation is 0.

Hopefully this helps you a little bit.

3. So, would the right thing for part C be to set $\displaystyle -(2x+y)/(2y+x)$ equal to zero and then solve for x and y?