Need to see if this is correct:
Find the slopes of the traces to z= 10-4x^2-y^2 at the point (2,1).

so i would take the partial derivatives of x and y then evaluate it..

$$\large f_x(x,y) = -8x$$
$$\large f_y(x,y) = -2y$$
$$\large f_x (2,1) =-16$$
$$\large f_y (2,1) = -2$$

Question

Need to see if this is correct:
Find the slopes of the traces to z= 10-4x^2-y^2   at the point (2,1).

so i would take the partial derivatives of x and y then evaluate it..

$$\large f_x(x,y) = -8x$$
$$\large f_y(x,y) = -2y$$
$$\large f_x (2,1) =-16$$
$$\large f_y (2,1) = -2$$

anonymous · Answer

I was thinking about the directional derivative but since no directional vector was give, i would assume the question is asking for the slope along the xz-plane or yz plane at the given point. So yes, that's correct

shamil98 · Answer

alright, thank you.

compassionate · Answer

Hi, 

Am I late? 

Your first two are the general formulas for the partial derivatives, then plugging in x = 2, y = 1, you get your answers at the specific point. (2,1)

shamil98 · Answer

a bit late yes, i got it lol 
Thank you anyways though.