Find the slopes of the surface $h ( x , y ) = 3 y ^ { 2 } - x ^ { 2 }$ in the x- and y- directions at the point $( - 1,3,26 )$ .
A)slope in x-direction: 29slope in y-direction: 17
B)slope in x-direction: 2slope in y-direction: 18
C)slope in x-direction: 17slope in y-direction: 29
D)slope in x-direction: 20slope in y-direction: 20
E)slope in x-direction: 18slope in y-direction: 2

Question

Quizplus · Accepted Answer

The slopes of the surface $h(x, y) = 3y^2 - x^2$ in the x- and y-directions at a point can be found by taking the partial derivatives of $h$ with respect to $x$ and $y$, respectively. For the x-direction: $\frac{\partial h}{\partial x} = -2x$. At the point $(-1,3,26)$, this becomes $-2(-1) = 2$.For the y-direction: $\frac{\partial h}{\partial y} = 6y$. At the point $(-1,3,26)$, this becomes $6(3) = 18$.Therefore, the slope in the x-direction is 2, and the slope in the y-direction is 18.

Find the Slopes of the Surface h(x,y)=3y2−x2h ( x , y ) = 3 y ^ { 2 } - x ^ { 2 }h(x,y)=3y2−x2

Find the Slopes of the Surface $h ( x , y ) = 3 y ^ { 2 } - x ^ { 2 }$