What is the extreme f(x)=(e^{ax}-e^{-ax})/(e^{ax)+e^{-ax}} ?

The extreme f(x)=(e^{ax}-e^{-ax})/(e^{ax)+e^{-ax}} is Saddle(0,0)

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extreme f(x)=(e^{ax}-e^{-ax})/(e^{ax)+e^{-ax}}

extreme

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{8 x ( e ^{x a} x - e ^{- x a} x )}{( e ^{x a} + e ^{- x a} ) ^{3}}

D (x, a) = \frac{64 e ^{2 x a} x a - 64 e ^{- 2 x a} x a - 16 e ^{2 x a} - 16 e ^{- 2 x a} - 32}{( e ^{x a} + e ^{- x a} ) ^{6}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

What is the extreme f(x)=(e^{ax}-e^{-ax})/(e^{ax)+e^{-ax}} ?
The extreme f(x)=(e^{ax}-e^{-ax})/(e^{ax)+e^{-ax}} is Saddle(0,0)