What is the extreme f(x,y)=-2x^2-y^3+9y^2+16x-15y+5 ?

The extreme f(x,y)=-2x^2-y^3+9y^2+16x-15y+5 is Saddle(4,1),Maximum(4,5)

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extreme f(x,y)=-2x^2-y^3+9y^2+16x-15y+5

extreme points

f (x, y) = - 2 x^{2} - y^{3} + 9 y^{2} + 16 x - 15 y + 5

Saddle (4, 1), Maximum (4, 5)

Solution steps

Find the critical points:

(4, 1), (4, 5)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6 y + 18

D (x, y) = - 4 (- 6 y + 18)

Check the sign of at each critical point

Check critical point

(4, 1) :

Saddle

Check critical point

(4, 5) :

Maximum

Saddle (4, 1), Maximum (4, 5)

f (x) = 2 x^{2} + \frac{91.2}{x}

P (a) = y^{2} - 4 r^{2} + r + e^{2}

f (t) = 25 cos (2 t)

f (x) = - 2 x^{3} + 24 x^{2} - 42 x + 7

f (x) = - 0.01 x^{2} + 120 x + 200000

What is the extreme f(x,y)=-2x^2-y^3+9y^2+16x-15y+5 ?
The extreme f(x,y)=-2x^2-y^3+9y^2+16x-15y+5 is Saddle(4,1),Maximum(4,5)