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4 votes
If


f(x) = {(ln \: x)}^(2)
at which of the following x values is the function both decreasing and concave up?

x = 0 \\ x = e \\ x = {e}^(2) \\ x = {e}^(3) \\ x = (1)/(e)


User SabreWolfy
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1 Answer

5 votes

Answer:


x = (1)/(e)

Explanation:


f(x) = {(lnx)}^(2)


f1st(x) = (2 lnx )/(x) = 0


x < 1 \: \: f1 < 0 \: \: de creasing


f2nd(x) = \frac{2 - 2 lnx}{ {x}^(2) } = 0


x < e \: \: f2 > 0 \: \: concave \: up

So x<1 is the condition which contains x=1/e

User CalvinDale
by
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