# Thread: rate of change with a elliptic paraboloid

1. ## rate of change with a elliptic paraboloid

Can someone help me solve this?

A point moves along the intersection of the elliptic paraboloid z=x^2+3y^2 and the plane x=2. At what rate is z changing with y when the point is at (2,1,7)?

2. Originally Posted by mike21
Can someone help me solve this?

A point moves along the intersection of the elliptic paraboloid z=x^2+3y^2 and the plane x=2. At what rate is z changing with y when the point is at (2,1,7)?
The rate of change is simply the derivative!

$\frac{ \partial z}{ \partial y }$

Which means we want the partial derivative with respect to y leaving x constant.

If $z = x^2+3y^2$ then $\frac{ \partial z}{ \partial y } = 6y$