Question

Find the derivative of \( f(x) = 3x^2 - 4x + 7 \).

• A. \( 6x - 4 \)
• B. \( 6x - 7 \)
• C. \( 3x - 4 \)
• D. \( 3x + 4 \)

Hint:

Remember: When differentiating, apply the power rule and handle constants separately (their derivative is 0).

Answer 1

The Correct Option is A

Step 1: Recall the power rule for differentiation
The derivative of \( f(x) = ax^n \) is given by: \[ \frac{d}{dx}(ax^n) = a \cdot n \cdot x^{n-1} \] Step 2: Differentiate the given function
We are given \( f(x) = 3x^2 - 4x + 7 \).
- The derivative of \( 3x^2 \) is \( 6x \) (using the power rule: \( 2 \cdot 3 = 6 \)), - The derivative of \( -4x \) is \( -4 \),
- The derivative of the constant \( 7 \) is \( 0 \).
So, the derivative of \( f(x) \) is: \[ f'(x) = 6x - 4 \] Answer: Therefore, the derivative of \( f(x) = 3x^2 - 4x + 7 \) is \( 6x - 4 \).
So, the correct answer is option (1).