Final answer:
The critical points of the function f(x) are found by differentiating and solving the resulting equation for x. Irrelevant information provided in the question is disregarded. The quadratic formula might be used if the derivative results in a quadratic equation.
Step-by-step explanation:
The question asks us to find the critical points of the function f(x) = x²√x - 16. To find the critical points, we need to calculate the derivative of the function and set it equal to zero, then solve for x. Note that the given information in the question does not directly relate to the function provided, which makes it irrelevant.
To solve for the derivative, we use the chain rule and the power rule. The function involves a combination of polynomial terms and a square root, which can be treated as a fractional power when differentiating. After finding the derivative, we might use the quadratic formula as a tool for determining the x-values at which the derivative is zero, thus finding the critical points of the function.