Given the function f (x) = 2Sin (ω x + π / 4) (ω > 0), the distance between the image of y = f (x) and two adjacent intersections of the line y = 2 is equal to π 1. Find the analytic expression of F (x); 2. Find the f (x) symmetry axis equation and monotone interval; 3. Find the maximum and minimum of F (x) in the interval [- π / 4, π / 2]

Because 2 is the maximum value of F (x), two adjacent maxima are separated by a period, so the period of F (x) is π, w = 2 (1) f (x) = 2Sin (2x + π / 4) (2) the axis of symmetry is a straight line passing through the fixed point perpendicular to the X axis, from 2x + π / 4 = k π + π / 2, x = k π / 2 + π / 8, K is an integer (3) when x is on [- π / 4, π / 2]

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