f =ln (1+2/x) is concave if x<-2?explain 

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Given `f=ln(1+2/x)` :

The domain of the function is `(-oo,-2)uu(0,oo)` . We are interested in the interval `(-oo,-2)` .



Note that the denominator is always positive. On the interval `(-oo,-2)` the numerator is always negative.

Thus the function is concave down for x<-2.