Final answer:
To determine the values of the function f(x) = 3x² - x³ at given points, each x value (-2, 0, 4) is substituted into the function, resulting in f(-2) = 20, f(0) = 0, and f(4) = -16.
Step-by-step explanation:
The student has given the function f(x) = 3x² - x³ and seeks to determine the values of f(-2), f(0), and f(4). To evaluate the function at these values of x, we substitute them into the function expression and simplify.
- For f(-2): f(-2) = 3(-2)² - (-2)³ = 3(4) - (-8) = 12 + 8 = 20.
- For f(0): f(0) = 3(0)² - (0)³ = 0 - 0 = 0.
- For f(4): f(4) = 3(4)² - (4)³ = 3(16) - 64 = 48 - 64 = -16.
Therefore, the values of the function at the given points are f(-2) = 20, f(0) = 0, and f(4) = -16.