rate of change with a elliptic paraboloid

Mar 2010
16
0
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)?
 
Apr 2010
384
153
Canada
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!

The question asks for,

\(\displaystyle \frac{ \partial z}{ \partial y } \)

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

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

Sub in your given point and you have your answer.