Given the function f (x) = 2cos (π 3 − x2) (1) find the monotone increasing interval of F (x); & nbsp; (2) find the maximum and minimum of F (x) if x ∈ [- π, π]

Given the function f (x) = 2cos (π 3 − x2) (1) find the monotone increasing interval of F (x); & nbsp; (2) find the maximum and minimum of F (x) if x ∈ [- π, π]

(1) The function f (x) = 2cos (π 3 − x2) = 2cos (x2 − π 3), let 2K - π ≤ x2 − π 3 ≤ 2K π K ∈ Z, then x ∈ [4K π − 4 π 3, 4K π + 2 π 3] & nbsp;, & nbsp; K ∈ Z, so the increasing interval of the function is: [4K π − 4 π 3, 4K π + 2 π 3] & nbsp;, & nbsp; K ∈ Z. (2) from X ∈ [- π, π], we can get x2 − π 3 ∈ [- 5 π 6, π 6], so when x2 − π 3 = - 5 π 6, the minimum value of function f (x) is - 3; when x2 − π 3 = 0, the maximum value of function f (x) is 2