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Show that f(x) = 3x + 1/3x is increasing in (1/3, 1) and decreasing in (1/9, 1/3)

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Show that f(x) = 3x + 1/3x is increasing in (1/3, 1) and decreasing in (1/9, 1/3)

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f(x) = 3x + 1/3x

Now, f is increasing if f'(x) > 0 and is decreasing if f'(x) < 0.

∴ f is decreasing in the interval \(\left(\frac{1}{9}, \,\frac{1}{3}\right).\)

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