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Homework Statement
attached.
Homework Equations
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?
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