Question

Find the slope of the surface in the x and y-directions at the given point. h(x,y) = x2 – y2 (-3, 2, 5)

Answer 1

If
`h(x,y)=x^2-y^2`, then you can find partial derivatives:

`(dh)/(dx) =2x \\ (dh)/(dy) =-2y`.

At point A(-3,2,5) (this is the point which lies on the surface, because
`5=(-3)^2-2^2=9-4=5`) these derivatives have values:


`(dh)/(dx) |_A=2\cdot (-3)=-6 \\ (dh)/(dy) =-2\cdot 2=-4` -- the slopes at x and y- directions, respectively.