What is the extreme f(x,y)= 1/3 x^3-5x^2-y^2-3y ?

The extreme f(x,y)= 1/3 x^3-5x^2-y^2-3y is Maximum(0,-3/2),Saddle(10,-3/2)

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extreme f(x,y)= 1/3 x^3-5x^2-y^2-3y

extreme

Maximum (0, - \frac{3}{2}), Saddle (10, - \frac{3}{2})

Solution steps

Find the critical points:

(0, - \frac{3}{2}), (10, - \frac{3}{2})

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

D (x, y) = - 2 (2 x - 10)

Check the sign of at each critical point

Check critical point

(0, - \frac{3}{2}) :

Maximum

Check critical point

(10, - \frac{3}{2}) :

Saddle

Maximum (0, - \frac{3}{2}), Saddle (10, - \frac{3}{2})

What is the extreme f(x,y)= 1/3 x^3-5x^2-y^2-3y ?
The extreme f(x,y)= 1/3 x^3-5x^2-y^2-3y is Maximum(0,-3/2),Saddle(10,-3/2)