Given the function f (x) = x, G (x) = 3 / 8x ^ 2 + LNX + 2. (1) find the maximum and minimum points of the function f (x) = g (x) - 2F (x)
F (x) = g (x) - 2F (x) = 3 / 8x ^ 2 + LNX + 2-2xf '(x) = 3 / 4x + 1 / X-2 = (3x ^ 2-8x + 4) / 4x = (3x-2) (X-2) / 4x Let f' (x) = 0 (3x-2) (X-2) = 0 x = 2 / 3 or x = 2x0 x > 2, f '(x) > 0 when x = 2 / 3, f (2 / 3) = ln (2 / 3) + 5 / 6x = 2 / 3, f (2) = ln2-1 / 2
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