f(x) = 18 - 12x - 12/x
f'(x) = -12 + 12 / x2
The critical points are given by f'(x) = -12 + 12 / x2 = 0
Hence, 12 / x2 = 12
Hence, x2 = 1
Hence, x = 1 or -1
However the given interval for x is (0, ∞)
x = -1 falls outside this interval, hence x = 1 is the only critical point in the given interval.
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