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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

f (x) = \frac{e ^{a x} - e ^{- a x}}{e ^{a x} + e ^{- a x}}

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)

x + ln (x^{2} + 1)

V (B, h) = \frac{B h}{3}

x^{3} + 3 x^{2} + 2 x

f (x) = (\frac{1}{x}) ln (x)

f (x) = - 8 sin (4 x)

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)