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).