- #1
miglo
- 98
- 0
Homework Statement
f(x,y)=5xy-7x^2+3x-6y+2
2. Homework Equations
(f_xx)(f_yy)-(f_xy)^2 the hessian or discriminant of f
The Attempt at a Solution
i arrived at a solution but i don't think its correct, and the answer isn't in the back of the book, so i just wanted to ask if i did this correctly
the first partial derivatives are f_x and f_Y are
f_x=5y-14x+3 and f_y=5x-6
setting f_y=0 i get x=6/5
plugging this value into f_x and solving for y i get 69/25
therefore my critical point is at (6/5,69/25)
the second order partial derivatives are then
f_xx=-14 f_yy=0 and f_xy=5
then using the discriminant of f i get -25 so i get a saddle point
but i graphed the function on wolfram alpha, and i doesn't seem like there is a saddle point on the graph
any help would be greatly appreciated, thanks