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

The extreme f(x,y)=ysqrt(x)-y^2-x+6y is Maximum(4,4)

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extreme f(x,y)=ysqrt(x)-y^2-x+6y

extreme points

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

Maximum (4, 4)

Solution steps

Find the critical points:

(4, 4)

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

D (x, y) = \frac{2 x y - x ^{\frac{3}{2}}}{4 x ^{\frac{5}{2}}}

Check the sign of at each critical point

Check critical point

(4, 4) :

Maximum

Maximum (4, 4)

f (x) = x^{3} - 6 x y + 8 y^{3}

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

f (x, y) = 5 x y - 7 x^{2} + 3 x - 6 y + 2

f (x) = \frac{x ^{2} - 16}{x ^{2} + 16}

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

What is the extreme f(x,y)=ysqrt(x)-y^2-x+6y ?
The extreme f(x,y)=ysqrt(x)-y^2-x+6y is Maximum(4,4)