Question

What are the critical points of `f(x,y)=x^3 y + 4x^2 − 8y`?

Answer 1

`(2, -4/3)`

Explanation:

`f_x(x,y) = 3x^2y+8x`

`f_y(x,y) = x^3-8`

Solve:
`3x^2y+8x = 0`

`x^3-8 = 0` `" "` so `x=2` now substitute in the other equation to get

`12y+16 = 0` `" "` so `y=-4/3`