What is the extreme y^3+x^3-21/2 y^2-3x+30y ?

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

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extreme y^3+x^3-21/2 y^2-3x+30y

extreme points

y^{3} + x^{3} - \frac{21}{2} y^{2} - 3 x + 30 y

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

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

(2, 1) :

Saddle

Check critical point

(2, - 1) :

Maximum

Check critical point

(5, 1) :

Minimum

Check critical point

(5, - 1) :

Saddle

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

f (x) = e^{8 x} + e^{- x}

f (x) = - 2 x^{2} + 4 x

g (x) = x^{3} - 3 x^{2} + 1

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

f (x, y) = 4 x y + \frac{2}{x} + \frac{1}{y}

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