Final answer:
The slope of the tangent line to the curve y=4³ at the point (−4,−256) is 192.
Step-by-step explanation:
The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. In this case, we are given the equation of the curve as y = 4³. To find the slope of the tangent line at the point (-4, -256), we need to find the derivative of the curve equation and evaluate it at x = -4.
The derivative of y = 4³ is dy/dx = 12x². Evaluating it at x = -4 gives us dy/dx = 12(-4)² = 192.
Therefore, the slope of the tangent line to the curve y = 4³ at the point (-4, -256) is 192.