What is the extreme f(x,y)=x2y ?

The extreme f(x,y)=x2y is Saddle(0,0)

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extreme f(x,y)=x2y

extreme points

f (x, y) = x 2 y

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

x^{2} + 4 x

4 x^{2} - 4 (8 - x)^{2}

f (x) = 3 x - 10 sin (\frac{x}{3}), 1 0^{\circ} \leq x \leq 3 8^{\circ}

f (x) = 9 x + \frac{3}{x}

f (x, y) = x^{2} + y^{2} - 16 x + 20 y - 5