Discuss the extremum of `f(x) = x^(2) + (1)/(x^(2))`

Discuss the extremum of f(x) = 2x^(3) - 3x^(2) - 12x + 5 for x in [-2, 4] and find the range of f(x) for the given interval.

Discuss the extremum of f(x) = sin x (1 + cos x), x in (0, pi//2) .

Discuss the extremum of f(x) = {{:(1 + sin x,x lt 0),(x^(2) - x + 1,x ge 0):} at x = 0.

Find the range of f(x) = cot^(-1)(2x - x^2)