It is known that the function f (x) is an even function defined on R. when x ≥ 0, f (x) = x2-4x. (1) find the value of F (- 1); (2) find the analytic expression of F (x); (3) find the minimum value of F (x) on [T, t + 1] (T > 0)

It is known that the function f (x) is an even function defined on R. when x ≥ 0, f (x) = x2-4x. (1) find the value of F (- 1); (2) find the analytic expression of F (x); (3) find the minimum value of F (x) on [T, t + 1] (T > 0)

(1) If x < 0, then - x > 0, f (x) = f (- x) = [(- x) 2-4 (- x)] = x2 + 4x (3) when x > 0, f (x) = x2-4x = (X-2) 2-4 is a decreasing function on (0,2) and an increasing function on (2, + ∞), i.e