Find all critical numbers for the function f(x) = -2x³ - 3x² + 12x + 1. Then, use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum.
a) Critical numbers: -3, 1, 2; Local max at x = -3, local min at x = 1 and x = 2
b) Critical numbers: -2, 1, 4; Local max at x = -2, local min at x = 1 and x = 4
c) Critical numbers: -3, 1, 4; Local max at x = -3, local min at x = 1 and x = 4
d) Critical numbers: -2, 2, 4; Local max at x = -2, local min at x = 2 and x = 4