The problem involves finding the slope of tangent lines to curves cut from the surface defined by the equation z = (3x^2) + (4y^2) - 6, specifically by planes that pass through the point (1,1,1) and are parallel to the xz and yz planes.
There appears to be some agreement on the definitions of slopes related to the planes, with participants confirming the relationships between the variables and the slopes. However, the discussion is still exploring the correct derivatives to use.
Participants are working under the assumption that the slopes are to be evaluated at the specific point (1,1,1) and are clarifying the implications of holding certain variables constant when determining the slopes.
So , slope of tnagent that parallel to xz planes is dz/dx , while the slope of tangent thatparallel to yz plane is dz /dy . ?FactChecker said:To be parallel to the xz plane means that the y value is some constant number (y ≡ 1). So there is no dy. y is not involved in that slope except that its constant value (1) might be in the equation. Calculate dz/dx and plug in the 1s.
Similarly, to be parallel to the yz plane means that the x value is some constant number (x ≡ 1). So there is no dx. x is not involved in that slope except that its constant value (1) might be in the equation. Calculate dz/dy and plug in the 1s
yeschetzread said:So
So , slope of tnagent that parallel to xz planes is dz/dx , while the slope of tangent thatparallel to yz plane is dz /dy . ?