What is the extreme f(y,z)=6yz-2y^2z-3yz^2 ?

The extreme f(y,z)=6yz-2y^2z-3yz^2 is Saddle(0,2),Maximum(1, 2/3)

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extreme f(y,z)=6yz-2y^2z-3yz^2

extreme points

f (y, z) = 6 yz - 2 y^{2} z - 3 y z^{2}

Saddle (0, 2), Maximum (1, \frac{2}{3})

Solution steps

Find the critical points:

(0, 2), (1, \frac{2}{3})

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

D (y, z) = - 24 yz + 48 y - 16 y^{2} + 72 z - 36 z^{2} - 36

Check the sign of at each critical point

Check critical point

(0, 2) :

Saddle

Check critical point

(1, \frac{2}{3}) :

Maximum

Saddle (0, 2), Maximum (1, \frac{2}{3})

f (x, y) = \frac{2 y + 3}{x y + 1}

f (x) = 4 x^{3} - 5 x^{2} + 3

P (x, y) = x^{2} + 6 x + 9 - 4 y^{2}

f (x) = x^{3} + 3 x^{2} - 9 x + 7

f (x) = 2 x^{3} + 9 x^{2} - 24 x + 5

What is the extreme f(y,z)=6yz-2y^2z-3yz^2 ?
The extreme f(y,z)=6yz-2y^2z-3yz^2 is Saddle(0,2),Maximum(1, 2/3)