What is the extreme f(x)=2x^3-y^2-6x+9y ?

The extreme f(x)=2x^3-y^2-6x+9y is Maximum(-1, 9/2),Saddle(1, 9/2)

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extreme f(x)=2x^3-y^2-6x+9y

extreme points

f (x) = 2 x^{3} - y^{2} - 6 x + 9 y

Maximum (- 1, \frac{9}{2}), Saddle (1, \frac{9}{2})

Solution steps

Find the critical points:

(- 1, \frac{9}{2}), (1, \frac{9}{2})

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

D (x, y) = - 24 x

Check the sign of at each critical point

Check critical point

(- 1, \frac{9}{2}) :

Maximum

Check critical point

(1, \frac{9}{2}) :

Saddle

Maximum (- 1, \frac{9}{2}), Saddle (1, \frac{9}{2})

f (x, y) = y \cdot e^{x^{2} - 2 y^{2}}

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

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

f (t) = (4 - t) 4^{t}

f (x) = 2 x^{3} - 15 x^{2} - 30

What is the extreme f(x)=2x^3-y^2-6x+9y ?
The extreme f(x)=2x^3-y^2-6x+9y is Maximum(-1, 9/2),Saddle(1, 9/2)