Find the slope of the surface in the \( x \) and \( y \)-directions at the given point. \[ \begin{array}{l}h(x, y)=x^{2}-y^{2} \\ (-2,2,0)\end{array} \]

To find the slope of the surface in the \( x \) and \( y \)-directions, we need to calculate the partial derivatives of the function \( h(x, y) = x^2 - y^2 \). First, let's calculate the partial derivative with respect to \( x \): \[ h_x(x, y) = \frac{\partial h}{\partial x} = 2x \] Next, we'll calculate the partial derivative with respect to \( y \): \[ h_y(x, y) = \frac{\partial h}{\partial y} = -2y \] Now, we can evaluate these derivatives at the point \( (-2, 2) \): For \( h_x \): \[ h_x(-2, 2) = 2(-2) = -4 \] For \( h_y \): \[ h_y(-2, 2) = -2(2) = -4 \] Thus, the slope of the surface at the point \( (-2, 2, 0) \) in the \( x \)-direction is \( -4 \) and in the \( y \)-direction is also \( -4 \).