Final answer:
To find the zeros of the function f(x) = -3x³ + 20x² - 36x + 16, set f(x) equal to 0 and solve for x using factoring, synthetic division, or the rational root theorem.
Step-by-step explanation:
The value 0 is a lower bound for the zeros of the function f(x) = -3x³ + 20x² - 36x + 16. To find the zeros of the function, we need to set f(x) equal to 0 and solve for x. In this case, setting f(x) = 0 gives us the equation -3x³ + 20x² - 36x + 16 = 0. To solve this equation, you can use factoring, synthetic division, or the rational root theorem.
Using the rational root theorem, we can find possible rational roots by finding the factors of the constant term (in this case, 16) and dividing them by the factors of the leading coefficient (in this case, -3).
After finding the possible rational roots, you can use a numerical or graphical method to approximate the actual zeros of the function.