Question

The function \( f(x) = 2x^3 - 3x^2 - 12x + 4 \), \( x \in \mathbb{R} \) has:

• A. two points of local maximum.
• B. two points of local minimum.
• C. one local maximum and one local minimum.
• D. neither maximum nor minimum.

Hint:

For a polynomial, find critical points by setting the first derivative to zero, then use the second derivative test to classify them as local maxima (\( f''(x)<0 \)) or minima (\( f''(x)>0 \)).