(a) Let f(x) = x³ + -2x+4. Find the absolute maximum and the absolute minimum of f on the closed interval [o, 2]. (b) Let f(x) = 12x5 + 15x* – 40x³ + 17. Find the critical numbers, and show what the...

Extracted text: (a) Let f(x) = x³ + -2x+4. Find the absolute maximum and the absolute minimum of f on the closed interval [o, 2]. (b) Let f(x) = 12x5 + 15x* – 40x³ + 17. Find the critical numbers, and show what the Second Derivative Test tells about their nature, that is local maximum, local minimum, neither, or nothing.