What is the extreme K(y,z)=3yz ?

The extreme K(y,z)=3yz is Saddle(0,0)

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extreme K(y,z)=3yz

extreme points

K (y, z) = 3 yz

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial y ^{2}} = 0

D (y, z) = - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

f (x) = \frac{x}{x}

f (x) = sec (x), - \frac{π}{6} \leq x \leq \frac{π}{3}

f (x) = \frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23

f (x) = x^{3} - (\frac{3}{2}) x^{2}