The function f is defined as `f(x) = -4x^(3) - 4x^(2)`. What is `f(-4)`?

Options

A. `-320`
B. `-192`
C. 16
D. 192

Answer

To find the value of \( f(-4) \) for the function \( f(x) = -4x^3 - 4x^2 \), we will substitute \( x = -4 \) into the function and simplify.

### Step-by-Step Solution:

1. **Write down the function**:
\[ f(x) = -4x^3 - 4x^2 \]

2. **Substitute \( x = -4 \)**:
\[ f(-4) = -4(-4)^3 - 4(-4)^2 \]

3. **Calculate \( (-4)^3 \)**:
\[ (-4)^3 = -64 \]
Therefore,
\[ -4(-4)^3 = -4(-64) = 256 \]

4. **Calculate \( (-4)^2 \)**:
\[ (-4)^2 = 16 \]
Therefore,
\[ -4(-4)^2 = -4(16) = -64 \]

5. **Combine the results**:
\[ f(-4) = 256 - 64 \]

6. **Final calculation**:
\[ f(-4) = 192 \]

Thus, the value of \( f(-4) \) is \( 192 \).