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Question
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
Solution
f(x) = `x + (25)/x`
∴ f'(x) = `d/dx(x + 25/x)`
= 1 + 25 (– 1)x–2
= `1 - (25)/x^2`
f is strictly decreasing if f'(x) < 0
i.e. if `1 - (25)/x^2 < 0`
i.e. if `1 < (25)/x^2`
i.e. if x2 < 25
i.e. if –5 < x < 5, x ≠ 0
i.e. if x ∈ (– 5, 5) – { 0 }
∴ f is strictly decreasing if x ∈ (– 5, 5) – { 0 }.
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