Final answer:
To find the points on the curve where the tangent is horizontal, set the derivative of the function equal to zero and solve for x. The points are (-1, 13) and (3, -4).
Step-by-step explanation:
To find the points on the curve where the tangent is horizontal, we need to find the values of x where the derivative of the function y = x³ - 3x² - 9x + 4 is equal to zero. The derivative of this function is 3x² - 6x - 9. Setting this equal to zero and solving for x, we get x = -1 and x = 3. Substituting these values back into the original function, we find that the points are (-1, 13) and (3, -4).