What does this symbol mean (partial derivatives)

[Firepanda]

Question : g(x,y) = x^3 - 3x^2 + 5xy - 7y^2

Verify that ∇g(0,0) = 0

I looked on wiki and it said the vector of partial derivatives, so my g(x,y) would become

∇g = (3x^2 - 6x + 5y, 5x -14y)

so what do i do from here? i don't see what its asking, do i plug x and y as 0 and show I get 0? Where do i plug them into?

 

[Defennder]

so what do i do from here? i don't see what its asking, do i plug x and y as 0 and show I get 0? Where do i plug them into?

You plug them into the expression for ∇g. That's what ∇g(0,0) mean. What would you get then? Note that your final answer is a vector.

 

[Firepanda]

You plug them into the expression for ∇g. That's what ∇g(0,0) mean. What would you get then? Note that your final answer is a vector.

so just a zero vector?

 

[Defennder]

Yes, that's what you should get as the question said.