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Question
Find the intervals of monotonicities and hence find the local extremum for the following functions:
f(x) = `x/(x - 5)`
Solution
f'(x) = `((x - 5)(1) - x(1))/(x - 5)^2`
= `- 5/(x - 5)^2`
f'(x) = 0, which is absured
But in f(x) = `x/(x - 5)`
The function is defined only when x < 5 or x > 5
∴ The intervals are `(-oo, 5)` and `(5, oo)`
In the interval `(-oo, 5)`, f'(x) < 0
In the interval `(5, oo)`, f'(x) < 0
∴ f(x) is strictly decreasing in `(-oo, 5)` and `(5, oo)`
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