Question:medium

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

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Remember: When differentiating, apply the power rule and handle constants separately (their derivative is 0).
Updated On: Nov 26, 2025
  • \( 6x - 4 \)
  • \( 6x - 7 \)
  • \( 3x - 4 \)
  • \( 3x + 4 \)
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The Correct Option is A

Solution and Explanation

Phase 1: Access the Power Rule of Differentiation
The general form of the derivative for \( f(x) = ax^n \) is established as:\[\frac{d}{dx}(ax^n) = a \cdot n \cdot x^{n-1}\]Phase 2: Compute the Derivative of the Specified Function
Given function: \( f(x) = 3x^2 - 4x + 7 \).
- Derivative of \( 3x^2 \): \( 6x \) (application of power rule: \( 2 \cdot 3 = 6 \)),- Derivative of \( -4x \): \( -4 \),
- Derivative of constant \( 7 \): \( 0 \).
Thus, the derivative of \( f(x) \) is computed as:\[f'(x) = 6x - 4\]Conclusion: Consequently, the derivative of \( f(x) = 3x^2 - 4x + 7 \) is \( 6x - 4 \).
The appropriate selection is option (1).
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