What is the extreme f(x,y)=3x-4xy+5y ?

The extreme f(x,y)=3x-4xy+5y is Saddle(5/4 , 3/4)

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extreme f(x,y)=3x-4xy+5y

extreme points

f (x, y) = 3 x - 4 x y + 5 y

Saddle (\frac{5}{4}, \frac{3}{4})

Solution steps

Find the critical points:

(\frac{5}{4}, \frac{3}{4})

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 16

Check the sign of at each critical point

Check critical point

(\frac{5}{4}, \frac{3}{4}) :

Saddle

Saddle (\frac{5}{4}, \frac{3}{4})

f (x) = x^{5} + 243

f (x) = 6 - \frac{x ^{3}}{3} + 15 x - x^{2}

f (x) = 3 x^{2} - 12 x + 7, 0 \leq x \leq 4

(x - 1)^{3} - 3 x

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

What is the extreme f(x,y)=3x-4xy+5y ?
The extreme f(x,y)=3x-4xy+5y is Saddle(5/4 , 3/4)