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Question
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
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Solution
`f(x) = x - 1/x`
`f'(x) = d/dx (x-1/x)`
`= 1-(-1/x^2)`
`= 1+1/x^2 > 0` for all x ∈ R, where x ≠ 0
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