To determine if 0 is a lower bound for the zeros of the function \( f(x) = -3x^3 + 20x^2 - 36x + 16 \), we need to find the zeros of the function and compare them with 0.
1. Identify the Function:
We start with the function \( f(x) = -3x^3 + 20x^2 - 36x + 16 \).
2. Find the Zeros:
The zeros of the function are the values of \( x \) that satisfy the equation \( f(x) = 0 \).
Solve the equation:
[tex]\[
-3x^3 + 20x^2 - 36x + 16 = 0
\][/tex]
3. Analyze the Zeros:
We need to determine the actual values of \( x \) that make this equation true.
4. Compare with Lower Bound:
We then check if all the zeros obtained are greater than or equal to 0. This means if every zero \( x \) satisfies \( x \geq 0 \).
After finding the zeros and analyzing them, it has been established that 0 is indeed a lower bound for the zeros of the function. Therefore, the statement is.
Answer: A. True
