What is the extreme f(x)=xy^2+3x^{-3x} ?

The extreme f(x)=xy^2+3x^{-3x} is Saddle(1/e ,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=xy^2+3x^{-3x}

extreme

Saddle (\frac{1}{e}, 0)

Solution steps

Find the critical points:

(\frac{1}{e}, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x

D (x, y) = - 4 y^{2} + \frac{- 18 + 54 x ( ln ( x ) + 1 ) ^{2}}{x ^{3 x}}

Check the sign of at each critical point

Check critical point

(\frac{1}{e}, 0) :

Saddle

Saddle (\frac{1}{e}, 0)

What is the extreme f(x)=xy^2+3x^{-3x} ?
The extreme f(x)=xy^2+3x^{-3x} is Saddle(1/e ,0)