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Show that graph of the function (x) =log...

Show that graph of the function (x) =`log_(e)(x-2)-(1)/(x)` always concave downwards.

Text Solution

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f(x) = `log_(e)(x-2)-(1)/(x),xlgt2`
`therefore f(x)=(1)/(x-2)+(1)/(x^(2))`
rarr `f(x)=-(1)/((x-2)^(2))-(2)/(x^(3))lt0`
Therefore ` f(x) is always concave downward.
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