# rate of change with a elliptic paraboloid

#### 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)?

#### AllanCuz

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!

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