help with tangent planes

[wet spoke]

how would I go about solving this>

[lucid dove]

so you have the partial derivatives at the point -3,9 based on the formula f(x,y)+∆xf_x + ∆yf_y
you have f_x at this point as 2 and f_y at this point as -⅓
which means you can form the vector ⟨2,-⅓⟩ which you can dot product with the direction vector you have
(5,3)-(-3,9)=(8,-6) and you gotta scale this into a unit vector:
√(64+36)=10
⟨0.8,-0.6⟩ which you now do:
⟨2,-⅓⟩•⟨0.8,-0.6⟩ which is:
1.6+0.2 or 1.8 as the slope

[wet spoke]

thank you!

[tropic hamlet]

@wet spoke has given 1 rep to @lucid dove

[lucid dove]

I've become your personal calc 3 helper lmao

[wet spoke]

I appreciate it lol