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 start with the function:
\[ f(x) = 2x^2 - 3x + 7 \]
To find the derivative \( f'(x) \), we differentiate each term with respect to \( x \):
- The derivative of \( 2x^2 \) is \( 4x \) (using the power rule).
- The derivative of \( -3x \) is \( -3 \).
- The derivative of the constant \( 7 \) is \( 0 \).

Thus, we have:
\[ f'(x) = 4x - 3 \]

### Step 2: Substitute \( x = -1 \) into the derivative
Now, we need to evaluate the derivative at \( x = -1 \):
\[ f'(-1) = 4(-1) - 3 \]
Calculating this gives:
\[ f'(-1) = -4 - 3 = -7 \]

### Conclusion
The derivative of \( f(x) = 2x^2 - 3x + 7 \) at \( x = -1 \) is:
\[ \boxed{-7} \]

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