finding critical points of a multivariable function

[molten harbor]

question asks to find critical points of this function and im rly lost on how to do that

[obsidian panther]

you set partial derivatives of x and y equal to 0 and you get two equations, and you find the solutions of the system, is the h an x actually?

[molten harbor]

its not thats the part thats been throwing me off

[obsidian panther]

what's the issue, calculating partial derivatives or being able to solve the system and find the critical points

[molten harbor]

i can get the partial derivatives but im lost after that

[foggy rover]

2x(y-2h)

you would treat h as any constant

[foggy rover]

thats if you differentiate with respect to x

if you differentiate with respect to y you get 2h+x^2-2y

then solve like a normal systems of equations treating h as an arbitrary constant

[molten harbor]

so are we just finding x and y values that allow the partial derivative to equal 0?

[foggy rover]

Exactly

[glad bramble]

.solved