What is the extreme f(x,y)=y^3+x^3-21/2 y^2-3x+30y ?

The extreme f(x,y)=y^3+x^3-21/2 y^2-3x+30y is Saddle(-1,5),Maximum(-1,2),Minimum(1,5),Saddle(1,2)

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extreme f(x,y)=y^3+x^3-21/2 y^2-3x+30y

extreme points

f (x, y) = y^{3} + x^{3} - \frac{21}{2} y^{2} - 3 x + 30 y

Saddle (- 1, 5), Maximum (- 1, 2), Minimum (1, 5), Saddle (1, 2)

Solution steps

Find the critical points:

(- 1, 5), (- 1, 2), (1, 5), (1, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y - 21

D (x, y) = 6 x (6 y - 21)

Check the sign of at each critical point

Check critical point

(- 1, 5) :

Saddle

Check critical point

(- 1, 2) :

Maximum

Check critical point

(1, 5) :

Minimum

Check critical point

(1, 2) :

Saddle

Saddle (- 1, 5), Maximum (- 1, 2), Minimum (1, 5), Saddle (1, 2)

f (x) = 4 x - 5

+ \frac{x + 1}{1 + \frac{1}{x + 1}}

f (x) = 5 x^{3} e^{- x}

f (x) = 2 x^{3} + 30 x^{2} + 144 x - 1

f (x) = sin^{2} (x), 0 \leq x \leq π

What is the extreme f(x,y)=y^3+x^3-21/2 y^2-3x+30y ?
The extreme f(x,y)=y^3+x^3-21/2 y^2-3x+30y is Saddle(-1,5),Maximum(-1,2),Minimum(1,5),Saddle(1,2)