Find the slope of the curve \( y=-10 x^{2} \) The slope of the curve \( y=-10 x^{2} \) at (

To find the slope of the curve \( y = -10x^2 \) at any given point, we first need to compute the derivative of the function. The derivative, or the slope of the curve, is given by: \[ \frac{dy}{dx} = -20x \] So, if you're looking for the slope at a specific point, simply substitute the x-coordinate of that point into the derivative. For example, if the point is (1, -10), then the slope at that point would be: \[ \frac{dy}{dx} \bigg|_{x=1} = -20(1) = -20 \] Now you know how to find the slope at any point on the curve! Imagine this parabola opening downwards; this creates a beautiful arch. Each point you pick offers a unique slope, painting a picture of how the curve behaves. Whether you're at the peak or down on the sides, those slopes tell a tale of slow descents and rapid falls! Keep that in mind as you dive deeper into calculus!