What is the extreme f(x,y)=6x-x^2+2y^4-16y^2+5 ?

The extreme f(x,y)=6x-x^2+2y^4-16y^2+5 is Maximum(3,0),Saddle(3,-2),Saddle(3,2)

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extreme f(x,y)=6x-x^2+2y^4-16y^2+5

extreme points

f (x, y) = 6 x - x^{2} + 2 y^{4} - 16 y^{2} + 5

Maximum (3, 0), Saddle (3, - 2), Saddle (3, 2)

Solution steps

Find the critical points:

(3, 0), (3, - 2), (3, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 24 y^{2} - 32

D (x, y) = - 2 (24 y^{2} - 32)

Check the sign of at each critical point

Check critical point

(3, 0) :

Maximum

Check critical point

(3, - 2) :

Saddle

Check critical point

(3, 2) :

Saddle

Maximum (3, 0), Saddle (3, - 2), Saddle (3, 2)

f (x) = x^{\frac{2}{3}} (20 - x)

y = x^{2} + 6 z + z^{2}

f (x) = (x - 1)^{2} (x - 3)

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

f (x) = tan (x) [- 5, 6]

What is the extreme f(x,y)=6x-x^2+2y^4-16y^2+5 ?
The extreme f(x,y)=6x-x^2+2y^4-16y^2+5 is Maximum(3,0),Saddle(3,-2),Saddle(3,2)