Calculus Worksheet: Differentiation

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1. Differentiate the following with respect to \(x\):
\( y = 4x^3 - 5x^2 + 8x - 2 \)

A) \( 12x^2 - 10x - 2 \) B) \( 12x^2 - 10x + 8 \) C) \( 4x^2 - 5x + 8 \) D) \( 12x^3 - 10x^2 + 8 \)

2. Differentiate the following with respect to \(x\):
\( y = 5x + \frac{3}{x^2} \)

A) \( 5 - \frac{6}{x^3} \) B) \( 5 + \frac{6}{x^3} \) C) \( 5 - \frac{3}{x^3} \) D) \( 1 - \frac{6}{x} \)

Note: Enter equations in the format y=mx+c without spaces (e.g., y=2x-4).

3. A curve has the equation \( y = 3x^2 - 7x + 2 \).
Find the equation of the tangent to the curve at the point (2, 0).

4. A curve has the equation \( y = 2x^3 - 3x^2 - 12x + 7 \).
Find the \(x\)-coordinates of the two stationary points.

\(x_1 =\) and \(x_2 =\)