Question

Find the derivative of the function: \[ f(x) = 3x^3 - 5x^2 + 2x - 4 \]

• A. \( 9x^2 - 10x + 2 \)
• B. \( 9x^2 - 10x + 1 \)
• C. \( 3x^2 - 5x + 2 \)
• D. \( 9x^2 - 5x + 2 \)

Hint:

Use the power rule to differentiate terms of the form \( ax^n \), where \( n \) is a constant.

Answer 1

The Correct Option is A

Step 1: Write the given function. The given function is: \[ f(x) = 3x^3 - 5x^2 + 2x - 4 \] Step 2: Use the power rule to differentiate. The power rule states that the derivative of \( ax^n \) is \( a \cdot n \cdot x^{n-1} \). Now differentiate each term of the function: \[ \frac{d}{dx}(3x^3) = 9x^2 \] \[ \frac{d}{dx}(-5x^2) = -10x \] \[ \frac{d}{dx}(2x) = 2 \] \[ \frac{d}{dx}(-4) = 0 \] Step 3: Combine the results. The derivative of \( f(x) \) is: \[ f'(x) = 9x^2 - 10x + 2 \] Answer: Therefore, the derivative is \( 9x^2 - 10x + 2 \).