Given that near (1,1,1) the curve of intersection of the surfaces
x^4 + y^2 + z^6 - 3xyz = 0 and xy + yz + zx - 3z^8 = 0
has the parametric equations x = f(t), y = g(t), z = t with f, g differentiable.
(a) What are the values of the derivatives f'(1), g'(1)?
(b) What is the tangent line to the curve of intersection at (1,1,1) given that z = 1 + s? (Find what x and y are equal to.)
Answers:
f'(1) = 4
g'(1) = 7
x = 1 + 4s
y = 1 + 7s

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