Final answer:
The slope of the curve y = x³ - 3 at any point is found by deriving the function with respect to x, yielding a slope formula of 3x². To find the slope at a specific point, substitute the x-value into this derivative.
Step-by-step explanation:
To find the slope of the curve y = x³ - 3, you must take the derivative of the function with respect to x. The derivative of x³ is 3x², and the derivative of a constant (in this case, -3) is zero. Therefore, the slope of the curve at any point x is given by 3x².
If you want to find the slope at a particular point, you just substitute the x-value of that point into the derivative. For example, to find the slope at x = 2, you would calculate 3(2)² which is 3 × 4, or 12.