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Question
Test whether the following function is increasing or decreasing.
f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0
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Solution
f'(x) = `7/"x" - 3`, x ∈ R, x ≠ 0
∴ f'(x) = `(-7)/"x"^2`
x ≠ 0, x2 > 0, i.e., `1/"x"^2 > 0`, i.e., `- 7/"x"^2 < 0`
∴ f'(x) < 0 for all x ∈ R, x ≠ 0
Hence, f(x) is a decreasing function, for all x ∈ R, x ≠ 0.
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