Final answer:
The slope of the curve y = x³ at the point x = 5 is found by calculating the derivative and substituting x = 5 into it, yielding a slope of 75.
Step-by-step explanation:
To determine the slope of the curve y = x³ at the point x = 5, we need to find the derivative of the function, as the derivative represents the slope of the tangent line at any given point on a curve. The derivative of y = x³ with respect to x is dy/dx = 3x². Now, substitute x = 5 into the derivative to find the slope at that specific point:
dy/dx at x = 5 = 3(5)² = 3(25) = 75.
Therefore, the slope of the curve y = x³ at the point x = 5 is 75.