(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

(f_xx)(f_yy)-(f_xy)^2 the hessian or discriminant of f

3. The attempt at a solution

i arrived at a solution but i dont think its correct, and the answer isnt 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 doesnt seem like there is a saddle point on the graph

any help would be greatly appreciated, thanks

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# Homework Help: Finding the local extrema or saddle points of a function

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