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Question 9 of 10

The value 0 is a lower bound for the zeros of the function shown below.

[tex]\[ f(x) = -3x^3 + 20x^2 - 36x + 16 \][/tex]

A. True
B. False


Sagot :

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
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