- #1

cathal84

- 15

- 0

## Homework Statement

Let f(x, y) = x^2 + kxy + y^2 , where k is some constant in R. i. Show that f has a stationary point at (0, 0) for every k ∈ R

## Homework Equations

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## The Attempt at a Solution

I may have the solution or i may have gone completely wrong I am not entirely sure.

i first found the derivative of f(x,y) with respect to x it was 2x+ky

then found the derivative of f(x,y) with respect to y it was 2y+kx

i then let both of them equal 0

then i solved 2x+ky=0 looking for a value of x and i got x=-ky/2

i then put this value for x back into 2y+kx=0 initially looking for a value of y but then i got y to cancel and i got a value for k instead. i got k=2.

so then i rewrote my derivatives as 2x+2y=0

and 2y+2x=0

which i have just realized are the same equation. anyway,

i then went ahead and tried to solve one of them for a value of x so i could sub it back

and i got x=-y

then i went and subbed this new value for x back into the equation and I am getting 0=0

have i answered the equation at all?

would greatly appreciate any input.

if i am completely wrong it would help greatly if someone pointed me in the right direction

thanks