Final answer:
The function f(x) = -8x³ - 24x² + 576x - 11 is concave upward.
Step-by-step explanation:
The function f(x) = -8x³ - 24x² + 576x - 11 is concave upward.
To determine the concavity of a function, we need to find its second derivative. Taking the first derivative, we get f'(x) = -24x² - 48x + 576. Then, taking the second derivative, we get f''(x) = -48x - 48.
Since the second derivative is negative for all values of x, the function is concave upward.