What is the extreme 7x-8y+2xy-x^2+y^3 ?

The extreme 7x-8y+2xy-x^2+y^3 is Saddle(23/6 , 1/3),Maximum(5/2 ,-1)

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extreme 7x-8y+2xy-x^2+y^3

extreme points

7 x - 8 y + 2 x y - x^{2} + y^{3}

Saddle (\frac{23}{6}, \frac{1}{3}), Maximum (\frac{5}{2}, - 1)

Solution steps

Find the critical points:

(\frac{23}{6}, \frac{1}{3}), (\frac{5}{2}, - 1)

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

D (x, y) = - 12 y - 4

Check the sign of at each critical point

Check critical point

(\frac{23}{6}, \frac{1}{3}) :

Saddle

Check critical point

(\frac{5}{2}, - 1) :

Maximum

Saddle (\frac{23}{6}, \frac{1}{3}), Maximum (\frac{5}{2}, - 1)

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

e^{x} (24 - 3 x^{2})

f (x, y) = - 8 x^{2} - 3 y^{2} + 8 x - y + 2

f (x) = - \frac{13}{x ^{2} - 5 x + 35}

f (x) = \frac{3 x ^{2} - 4 x y + 2 y ^{2}}{4 x + 9 y ^{2}}

What is the extreme 7x-8y+2xy-x^2+y^3 ?
The extreme 7x-8y+2xy-x^2+y^3 is Saddle(23/6 , 1/3),Maximum(5/2 ,-1)