What is the extreme f(x,y)=(x-5)(30-6x+4y)+(y-12)(80+8x-7y) ?

The extreme f(x,y)=(x-5)(30-6x+4y)+(y-12)(80+8x-7y) is Maximum(51,54)

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extreme f(x,y)=(x-5)(30-6x+4y)+(y-12)(80+8x-7y)

extreme points

f (x, y) = (x - 5) (30 - 6 x + 4 y) + (y - 12) (80 + 8 x - 7 y)

Maximum (51, 54)

Solution steps

Find the critical points:

(51, 54)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 14

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(51, 54) :

Maximum

Maximum (51, 54)

f (x) = - 0.001 x^{2} + 3.4 x - 40

\frac{sin ( 5 x )}{sin ^{5} ( x )}

f (x) = \frac{x ^{2} - 2 x + 1}{x - 4}

f (x) = \frac{x ^{2} - 2 x + 1}{x - 2}

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

What is the extreme f(x,y)=(x-5)(30-6x+4y)+(y-12)(80+8x-7y) ?
The extreme f(x,y)=(x-5)(30-6x+4y)+(y-12)(80+8x-7y) is Maximum(51,54)