Find values of the constant a, b, and c such that the directional derivative of f(x, y, z) = ax(y^2) + byz + c(z^2)(x^3) at the point (1, 2, -1) has a maximum value of 64 in a direction parallel to the z-axis.
What I tried doing was that since the direction is in the z-axis, this is a partial derivative. So I took D3f(x, y, z) and set it to less than or equal to 64. Then I'm stuck. Any ideas?