If `f(x)=2x^(2)," find "(f(3*8)-f(4))/(3*8-4):`

Options

A. `1*56`
B. `156`
C. `15*6`
D. `0*156`

Answer

To solve the problem, we need to evaluate the expression \(\frac{f(3.8) - f(4)}{3.8 - 4}\) given that \(f(x) = 2x^2\).

### Step-by-Step Solution:

1. **Calculate \(f(3.8)\)**:
\[ f(3.8) = 2 \times (3.8)^2 \]
First, calculate \((3.8)^2\):
\[ (3.8)^2 = 14.44 \]
Now, substitute back into the function:
\[ f(3.8) = 2 \times 14.44 = 28.88 \]

2. **Calculate \(f(4)\)**:
\[ f(4) = 2 \times (4)^2 \]
Calculate \((4)^2\):
\[ (4)^2 = 16 \]
Now, substitute back into the function:
\[ f(4) = 2 \times 16 = 32 \]

3. **Substitute the values into the expression**:
Now we substitute \(f(3.8)\) and \(f(4)\) into the expression:
\[ \frac{f(3.8) - f(4)}{3.8 - 4} = \frac{28.88 - 32}{3.8 - 4} \]

4. **Calculate the numerator**:
\[ 28.88 - 32 = -3.12 \]

5. **Calculate the denominator**:
\[ 3.8 - 4 = -0.2 \]

6. **Combine the results**:
Now we can substitute the values into the expression:
\[ \frac{-3.12}{-0.2} \]

7. **Simplify the fraction**:
Dividing the numerator by the denominator:
\[ \frac{-3.12}{-0.2} = 15.6 \]

### Final Answer:
The final result is:
\[ \boxed{15.6} \]