What is the extreme f(x,y)=(x^2-5y^2)e^x ?

The extreme f(x,y)=(x^2-5y^2)e^x is Saddle(0,0),Maximum(-2,0)

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extreme f(x,y)=(x^2-5y^2)e^x

extreme points

f (x, y) = (x^{2} - 5 y^{2}) e^{x}

Saddle (0, 0), Maximum (- 2, 0)

Solution steps

Find the critical points:

(0, 0), (- 2, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 10 e^{x}

D (x, y) = - 10 e^{2 x} x^{2} - 40 e^{2 x} x - 50 e^{2 x} y^{2} - 20 e^{2 x}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 2, 0) :

Maximum

Saddle (0, 0), Maximum (- 2, 0)

What is the extreme f(x,y)=(x^2-5y^2)e^x ?
The extreme f(x,y)=(x^2-5y^2)e^x is Saddle(0,0),Maximum(-2,0)