What is the extreme 4xy+2y-3x^2+3x-4y^2 ?

The extreme 4xy+2y-3x^2+3x-4y^2 is Maximum(1, 3/4)

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extreme 4xy+2y-3x^2+3x-4y^2

extreme points

4 x y + 2 y - 3 x^{2} + 3 x - 4 y^{2}

Maximum (1, \frac{3}{4})

Solution steps

Find the critical points:

(1, \frac{3}{4})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 8

D (x, y) = 32

Check the sign of at each critical point

Check critical point

(1, \frac{3}{4}) :

Maximum

Maximum (1, \frac{3}{4})

y = 2 x^{2} - 8 x + 10

x^{2} - 2 x - 3

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

f (x) = x^{3} e^{- 3 x}

f (x, y) = y^{3} + 3 x^{2} y - 6 x y + 1

What is the extreme 4xy+2y-3x^2+3x-4y^2 ?
The extreme 4xy+2y-3x^2+3x-4y^2 is Maximum(1, 3/4)