Final answer:
To find the absolute maximum of y = (x^2 - 1)^3 on the interval [-1, 2], evaluate the function at its critical points and endpoints. The absolute maximum value is 1, which occurs at x = 0.
Step-by-step explanation:
To find the absolute maximum of the function y = (x^2 - 1)^3 on the interval [-1, 2], we need to evaluate the function at its critical points and endpoints. First, we find the derivative of the function which is y' = 3(x^2 - 1)^2 * 2x. Setting y' to zero, we get x = -1, 0, and 1 as the critical points. Testing the function at these points and the endpoints, we find that y(-1) = 0, y(0) = 1, and y(1) = 0. Therefore, the absolute maximum value of y is 1, which occurs at x = 0.