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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

extreme points

f (x) e^{2 x} (x^{2} - 3 x + 2)

Saddle (0, 0), Saddle (0, 2), Saddle (0, 1)

Solution steps

Find the critical points:

(0, 0), (0, 2), (0, 1)

\frac{\partial ^{2} f}{\partial f ^{2}} = f (4 e^{2 x} x^{3} - 10 e^{2 x} x + 2 e^{2 x})

D (f, x) = - e^{4 x} (2 x^{3} - 3 x^{2} - 2 x + 2)^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(0, 2) :

Saddle

Check critical point

(0, 1) :

Saddle

Saddle (0, 0), Saddle (0, 2), Saddle (0, 1)

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