1. The problem statement, all variables and given/known data attached. 2. Relevant equations 3. The attempt at a solution I thought the problem was easy, but my answer is wrong (aparently; I still disagree.) First I defined x = (y^3)(z^3) to be a surface of function F So F(x,y,z) = (y^3)(z^3) - x = 0 Then, the gradient of F: Partial wrt x = -1 Partial wrt y = 3y^2(z^3) Partial wrt z = 3z^2(y^3) Gradient F = -1i + 3y^2(z^3)j + 3z^2(y^3)k Gradient F(1,-1,-1) = -1i + 3(-1)^2((-1)^3)j + 3(-1)^2((-1)^3)k = -i - 3j - 3k Then the tangent plane formula is - x - 3y - 3z = 5 or x + 3y + 3z = -5 Where am I going wrong with this?