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