What is the extreme F(x,y)=x*y+(pi*(x/2)^2)/2 ?

The extreme F(x,y)=x*y+(pi*(x/2)^2)/2 is Saddle(0,0)

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extreme F(x,y)=xy+(pi(x/2)^2)/2

extreme points

F (x, y) = x \cdot y + \frac{π \cdot ( \frac{x}{2} ) ^{2}}{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = - \frac{5 x ^{4}}{4} - \frac{4 x ^{3}}{3} - 4

f (x) = 4 (z^{- x}) + 1

y = 15 x e^{- x}

f (x) = x^{2} + 6

f (x) = 6 x^{2} + 1 - x, 0 \leq x \leq 3

What is the extreme F(x,y)=x*y+(pi*(x/2)^2)/2 ?
The extreme F(x,y)=x*y+(pi*(x/2)^2)/2 is Saddle(0,0)