The derivative of `f(x) = 2x^(2) - 3x + 7` at x = - 1 is

Options

A. 7
B. `-7`
C. 6
D. 12

Answer

To find the derivative of the function \( f(x) = 2x^2 - 3x + 7 \) at \( x = -1 \), we will follow these steps:

### Step 1: Differentiate the function
We will use the power rule of differentiation, which states that the derivative of \( x^n \) is \( n \cdot x^{n-1} \).

1. Differentiate \( 2x^2 \):
\[ \frac{d}{dx}(2x^2) = 2 \cdot 2x^{2-1} = 4x \]

2. Differentiate \( -3x \):
\[ \frac{d}{dx}(-3x) = -3 \]

3. Differentiate the constant \( 7 \):
\[ \frac{d}{dx}(7) = 0 \]

Combining these results, we find the derivative of \( f(x) \):
\[ f'(x) = 4x - 3 \]

### Step 2: Evaluate the derivative at \( x = -1 \)
Now, we will substitute \( x = -1 \) into the derivative we found:
\[ f'(-1) = 4(-1) - 3 \]
Calculating this gives:
\[ f'(-1) = -4 - 3 = -7 \]

### Final Answer
Thus, the derivative of \( f(x) = 2x^2 - 3x + 7 \) at \( x = -1 \) is:
\[ \boxed{-7} \]