Gradient of the Curve y = 2x²–5x² – 3x at x = 0

To find the gradient of the curve y = 2x²–5x² – 3x at x = 0, we need to differentiate the equation with respect to x and then substitute x = 0.

Step 1: Differentiate the equation with respect to x

y = 2x²–5x² – 3x

dy/dx = 4x – 10x – 3

dy/dx = -6x – 3

Step 2: Substitute x = 0

dy/dx = -6(0) – 3

dy/dx = -3

Therefore, the gradient of the curve y = 2x²–5x² – 3x at x = 0 is -3.

Explanation:

- The gradient of a curve at a point is the slope of the tangent to the curve at that point.
- To find the gradient of a curve at a point, we differentiate the equation of the curve with respect to x, substitute the value of x at the given point, and then evaluate the derivative.
- In this case, we differentiate y = 2x²–5x² – 3x with respect to x and get dy/dx = -6x – 3.
- Then we substitute x = 0 to get dy/dx = -3.
- Therefore, the gradient of the curve y = 2x²–5x² – 3x at x = 0 is -3.