The gradient of a curve at a given point represents the slope of the curve at that point. To find the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0, we need to differentiate the equation with respect to x, and then substitute x = 0 into the derivative.

Differentiating the equation y = 2x^3 - 3x^2 - 12x + 8 with respect to x will give us the gradient function, denoted as dy/dx, which represents the rate of change of y with respect to x.

Below is the step-by-step process to find the gradient of the curve:

1. Differentiate the equation y = 2x^3 - 3x^2 - 12x + 8 with respect to x. Each term in the equation is differentiated separately using the power rule of differentiation.

- The derivative of 2x^3 with respect to x is 6x^2.
- The derivative of -3x^2 with respect to x is -6x.
- The derivative of -12x with respect to x is -12.
- The derivative of 8 with respect to x is 0 (as it is a constant term).

Therefore, the derivative of y = 2x^3 - 3x^2 - 12x + 8 with respect to x is dy/dx = 6x^2 - 6x - 12.

2. Substitute x = 0 into the derivative dy/dx to find the gradient of the curve at x = 0.

When x = 0, the derivative becomes dy/dx = 6(0)^2 - 6(0) - 12 = 0 - 0 - 12 = -12.

Hence, the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0 is -12.

In summary, the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0 is -12.

The cost function of a company is given by (x)=100x-8x