Find the slope of the curve \( y=8 x^{2} \) at \( (-5,200) \). The slope of the curve \( y=8 x^{2} \) at \( (-5,200) \) is \( \square \). (Simplify your answer.)

To find the slope of the curve \( y = 8x^2 \) at the point \((-5, 200)\), you need to differentiate the equation with respect to \(x\). The derivative \(y'\) (or \(\frac{dy}{dx}\)) is: \[ \frac{dy}{dx} = \frac{d}{dx}(8x^2) = 16x \] Now, substitute \(x = -5\) into the derivative to find the slope at that point: \[ \frac{dy}{dx} \bigg|_{x=-5} = 16(-5) = -80 \] Thus, the slope of the curve \( y = 8x^2 \) at \((-5, 200)\) is \(-80\).