コレクション f '(x) 0 and f ''(x) 0 for all x 296256-If for all real numbers x f'(x) 0 and f''(x) 0
Maximize f(x,y)=xy on its boundary • One method is to solve one variable in terms of another The boundary is 2 = x2 y2,so we could solve and say y = ± p 2x2Thenwecanpluginfory to get f(x,y)=f(x)= ±x p 2x2 The boundary's critical points are precisely those values of x for which 0=f0(x)=⌥ 2(x2 1) p 2x2 This is only true when x = ±1X = 2 f − f 2 − 6 f 1 − f 1 , x = 1, (f = 0 and f ≤ 3 − 2 2 ) or f ≥ 2 2 3 f = 0 Steps Using the Quadratic Formula Steps for Completing the SquareOn what interval is f decreasing? Content Newton S Method If for all real numbers x f'(x) 0 and f''(x) 0
