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Show that f(x) = e^(1//x) is a strictly ...

Show that `f(x) = e^(1//x)` is a strictly decreasing function for all `x gt 0`

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`f(x) = e^(1//x) rArr f'(x) = - (1)/(x^(2)) e^(1//x) lt 0 " for all " x gt 0`
`[ :' x^(2) gt 0 adn e^(1//x) gt 0 " when " x gt 0]`
Thus, `f'(x) lt 0 " for all " x gt 0`
Hence, f(x) is strictly decreasing for all `x gt 0`
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