Question

Find the slope of a line tangent to the surface z+x^2+y2-3=0 and parallel to the xz plane

Answer 1

Answer:

Slope in the direction of x:

$\frac{\partial }{\partial x}\left(-x^2-y^2+3\right)=-2x$

Since I differentiate in the direction of x and the output of the original function is z, all the tangent lines should be parallel to to xz plane.

Hope this is correct and hope it helps :)

Step-by-step explanation: