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 points

f (x, y) = \frac{1}{3} x^{3} - 5 x^{2} - y^{2} - 3 y

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})

f (x) = \frac{x ^{2} - 1}{x + 1}

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

g (x) = x (x - 1)^{2}

y = x^{3} - 12 x

f (x) = t^{3} - 13 t^{2} + 50 t - 56

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)