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Popular Functions >

extreme ye^{x^2-y^2}

Solution

extreme

Solution

Saddle (- \frac{1}{2}, 0), Saddle (\frac{1}{2}, 0), Saddle (- \frac{1}{2}, 0), Saddle (\frac{1}{2}, 0)

Solution steps

Find the critical points:

(- \frac{1}{2}, 0), (\frac{1}{2}, 0), (- \frac{1}{2}, 0), (\frac{1}{2}, 0)

\frac{\partial ^{2} f}{\partial y ^{2}} = 2 y (2 e^{x^{2} - y^{2}} x^{2} + e^{x^{2} - y^{2}})

D (y, x) = 2 y (4 e^{(y + x) (- y + x)} y^{3} - 6 e^{(y + x) (- y + x)} y) (2 e^{x^{2} - y^{2}} x^{2} + e^{x^{2} - y^{2}}) - 4 e^{2 (y + x) (- y + x)} x^{2} (2 y + 1)^{2} (2 y - 1)^{2}

Check the sign of at each critical point

Check critical point

(- \frac{1}{2}, 0) :

Saddle

Check critical point

(\frac{1}{2}, 0) :

Saddle

Check critical point

(- \frac{1}{2}, 0) :

Saddle

Check critical point

(\frac{1}{2}, 0) :

Saddle

Saddle (- \frac{1}{2}, 0), Saddle (\frac{1}{2}, 0), Saddle (- \frac{1}{2}, 0), Saddle (\frac{1}{2}, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme ye^{x^2-y^2} ?
The extreme ye^{x^2-y^2} is